diff --git a/api/all-features.txt b/api/all-features.txt
index 648605452..34562bf4e 100644
--- a/api/all-features.txt
+++ b/api/all-features.txt
@@ -21,8 +21,10 @@
 impl !core::panic::unwind_safe::RefUnwindSafe for bech32::EncodeIoError
 impl !core::panic::unwind_safe::UnwindSafe for bech32::EncodeIoError
 impl bech32::primitives::ExtensionField for bech32::primitives::gf32_ext::Fe1024
+impl bech32::primitives::ExtensionField for bech32::primitives::gf32_ext::Fe32768
 impl bech32::primitives::Field for bech32::primitives::gf32::Fe32
 impl bech32::primitives::Field for bech32::primitives::gf32_ext::Fe1024
+impl bech32::primitives::Field for bech32::primitives::gf32_ext::Fe32768
 impl bech32::primitives::checksum::Checksum for bech32::primitives::Bech32
 impl bech32::primitives::checksum::Checksum for bech32::primitives::Bech32m
 impl bech32::primitives::checksum::Checksum for bech32::primitives::NoChecksum
@@ -337,42 +339,58 @@ impl core::ops::arith::Add<&bech32::primitives::gf32::Fe32> for &bech32::primiti
 impl core::ops::arith::Add<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Add<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Add<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Add<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::AddAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::AddAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::AddAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::AddAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Div for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<&bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Div<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Div<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::DivAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::DivAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::DivAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::DivAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Mul for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<&bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Mul<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Mul<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::MulAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::MulAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::MulAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::MulAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Neg for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<&bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Sub<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Sub<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::SubAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::SubAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::SubAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::SubAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::bit::BitXor for bech32::primitives::checksum::PackedNull
 impl core::panic::unwind_safe::RefUnwindSafe for bech32::DecodeError
 impl core::panic::unwind_safe::RefUnwindSafe for bech32::EncodeError
@@ -746,6 +764,14 @@ pub const bech32::primitives::gf32_ext::Fe1024::MULTIPLICATIVE_ORDER_FACTORS: &'
 pub const bech32::primitives::gf32_ext::Fe1024::ONE: Self
 pub const bech32::primitives::gf32_ext::Fe1024::POLYNOMIAL: Self
 pub const bech32::primitives::gf32_ext::Fe1024::ZERO: Self
+pub const bech32::primitives::gf32_ext::Fe32768::DEGREE: usize
+pub const bech32::primitives::gf32_ext::Fe32768::EXT_ELEM: Self
+pub const bech32::primitives::gf32_ext::Fe32768::GENERATOR: Self
+pub const bech32::primitives::gf32_ext::Fe32768::MULTIPLICATIVE_ORDER: usize
+pub const bech32::primitives::gf32_ext::Fe32768::MULTIPLICATIVE_ORDER_FACTORS: &'static [usize]
+pub const bech32::primitives::gf32_ext::Fe32768::ONE: Self
+pub const bech32::primitives::gf32_ext::Fe32768::POLYNOMIAL: Self
+pub const bech32::primitives::gf32_ext::Fe32768::ZERO: Self
 pub const bech32::primitives::hrp::BC: bech32::primitives::hrp::Hrp
 pub const bech32::primitives::hrp::BCRT: bech32::primitives::hrp::Hrp
 pub const bech32::primitives::hrp::TB: bech32::primitives::hrp::Hrp
@@ -781,6 +807,14 @@ pub fn &bech32::primitives::gf32_ext::Fe1024::mul(self, other: &bech32::primitiv
 pub fn &bech32::primitives::gf32_ext::Fe1024::mul(self, other: bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
 pub fn &bech32::primitives::gf32_ext::Fe1024::sub(self, other: &bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
 pub fn &bech32::primitives::gf32_ext::Fe1024::sub(self, other: bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
+pub fn &bech32::primitives::gf32_ext::Fe32768::add(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::add(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::div(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::div(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::mul(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::mul(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::sub(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::sub(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
 pub fn &bech32::primitives::gf32_ext::Fe32Ext<DEG>::mul(self, other: &bech32::primitives::gf32::Fe32) -> Self::Output
 pub fn &bech32::primitives::gf32_ext::Fe32Ext<DEG>::mul(self, other: bech32::primitives::gf32::Fe32) -> Self::Output
 pub fn bech32::ByteIterExt::bytes_to_fes(self) -> bech32::primitives::iter::BytesToFes<Self>
@@ -1021,6 +1055,20 @@ pub fn bech32::primitives::gf32_ext::Fe1024::mul_assign(&mut self, other: &bech3
 pub fn bech32::primitives::gf32_ext::Fe1024::multiplicative_inverse(self) -> Self
 pub fn bech32::primitives::gf32_ext::Fe1024::sub(self, other: &bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
 pub fn bech32::primitives::gf32_ext::Fe1024::sub_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe1024)
+pub fn bech32::primitives::gf32_ext::Fe32768::_add(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_div(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_mul(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_neg(self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_sub(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::add(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::add_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
+pub fn bech32::primitives::gf32_ext::Fe32768::div(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::div_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
+pub fn bech32::primitives::gf32_ext::Fe32768::mul(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::mul_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
+pub fn bech32::primitives::gf32_ext::Fe32768::multiplicative_inverse(self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::sub(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::sub_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
 pub fn bech32::primitives::gf32_ext::Fe32Ext<DEG>::clone(&self) -> bech32::primitives::gf32_ext::Fe32Ext<DEG>
 pub fn bech32::primitives::gf32_ext::Fe32Ext<DEG>::eq(&self, other: &bech32::primitives::gf32_ext::Fe32Ext<DEG>) -> bool
 pub fn bech32::primitives::gf32_ext::Fe32Ext<DEG>::fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result
@@ -1180,9 +1228,11 @@ pub trait bech32::primitives::iter::ByteIterExt: core::marker::Sized + core::ite
 pub trait bech32::primitives::iter::Fe32IterExt: core::marker::Sized + core::iter::traits::iterator::Iterator<Item = bech32::primitives::gf32::Fe32>
 pub type &bech32::primitives::gf32::Fe32::Output = bech32::primitives::gf32::Fe32
 pub type &bech32::primitives::gf32_ext::Fe1024::Output = bech32::primitives::gf32_ext::Fe32Ext<2>
+pub type &bech32::primitives::gf32_ext::Fe32768::Output = bech32::primitives::gf32_ext::Fe32Ext<3>
 pub type &bech32::primitives::gf32_ext::Fe32Ext<DEG>::Output = bech32::primitives::gf32_ext::Fe32Ext<DEG>
 pub type bech32::Checksum::MidstateRepr: bech32::primitives::checksum::PackedFe32
 pub type bech32::Fe1024 = bech32::primitives::gf32_ext::Fe32Ext<2>
+pub type bech32::Fe32768 = bech32::primitives::gf32_ext::Fe32Ext<3>
 pub type bech32::primitives::Bech32::MidstateRepr = u32
 pub type bech32::primitives::Bech32m::MidstateRepr = u32
 pub type bech32::primitives::ExtensionField::BaseField: bech32::primitives::Field
@@ -1201,6 +1251,9 @@ pub type bech32::primitives::gf32::Fe32::Output = bech32::primitives::gf32::Fe32
 pub type bech32::primitives::gf32_ext::Fe1024 = bech32::primitives::gf32_ext::Fe32Ext<2>
 pub type bech32::primitives::gf32_ext::Fe1024::BaseField = bech32::primitives::gf32::Fe32
 pub type bech32::primitives::gf32_ext::Fe1024::Output = bech32::primitives::gf32_ext::Fe32Ext<2>
+pub type bech32::primitives::gf32_ext::Fe32768 = bech32::primitives::gf32_ext::Fe32Ext<3>
+pub type bech32::primitives::gf32_ext::Fe32768::BaseField = bech32::primitives::gf32::Fe32
+pub type bech32::primitives::gf32_ext::Fe32768::Output = bech32::primitives::gf32_ext::Fe32Ext<3>
 pub type bech32::primitives::gf32_ext::Fe32Ext<DEG>::Output = bech32::primitives::gf32_ext::Fe32Ext<DEG>
 pub type bech32::primitives::hrp::ByteIter<'b>::Item = u8
 pub type bech32::primitives::hrp::CharIter<'b>::Item = char
diff --git a/api/alloc-only.txt b/api/alloc-only.txt
index b09a4ab9a..a13fc1f5f 100644
--- a/api/alloc-only.txt
+++ b/api/alloc-only.txt
@@ -18,8 +18,10 @@
 #[repr(transparent)] pub struct bech32::Fe32(_)
 #[repr(transparent)] pub struct bech32::primitives::gf32::Fe32(_)
 impl bech32::primitives::ExtensionField for bech32::primitives::gf32_ext::Fe1024
+impl bech32::primitives::ExtensionField for bech32::primitives::gf32_ext::Fe32768
 impl bech32::primitives::Field for bech32::primitives::gf32::Fe32
 impl bech32::primitives::Field for bech32::primitives::gf32_ext::Fe1024
+impl bech32::primitives::Field for bech32::primitives::gf32_ext::Fe32768
 impl bech32::primitives::checksum::Checksum for bech32::primitives::Bech32
 impl bech32::primitives::checksum::Checksum for bech32::primitives::Bech32m
 impl bech32::primitives::checksum::Checksum for bech32::primitives::NoChecksum
@@ -308,42 +310,58 @@ impl core::ops::arith::Add<&bech32::primitives::gf32::Fe32> for &bech32::primiti
 impl core::ops::arith::Add<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Add<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Add<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Add<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::AddAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::AddAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::AddAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::AddAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Div for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<&bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Div<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Div<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::DivAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::DivAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::DivAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::DivAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Mul for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<&bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Mul<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Mul<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::MulAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::MulAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::MulAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::MulAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Neg for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<&bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Sub<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Sub<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::SubAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::SubAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::SubAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::SubAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::bit::BitXor for bech32::primitives::checksum::PackedNull
 impl core::panic::unwind_safe::RefUnwindSafe for bech32::DecodeError
 impl core::panic::unwind_safe::RefUnwindSafe for bech32::EncodeError
@@ -715,6 +733,14 @@ pub const bech32::primitives::gf32_ext::Fe1024::MULTIPLICATIVE_ORDER_FACTORS: &'
 pub const bech32::primitives::gf32_ext::Fe1024::ONE: Self
 pub const bech32::primitives::gf32_ext::Fe1024::POLYNOMIAL: Self
 pub const bech32::primitives::gf32_ext::Fe1024::ZERO: Self
+pub const bech32::primitives::gf32_ext::Fe32768::DEGREE: usize
+pub const bech32::primitives::gf32_ext::Fe32768::EXT_ELEM: Self
+pub const bech32::primitives::gf32_ext::Fe32768::GENERATOR: Self
+pub const bech32::primitives::gf32_ext::Fe32768::MULTIPLICATIVE_ORDER: usize
+pub const bech32::primitives::gf32_ext::Fe32768::MULTIPLICATIVE_ORDER_FACTORS: &'static [usize]
+pub const bech32::primitives::gf32_ext::Fe32768::ONE: Self
+pub const bech32::primitives::gf32_ext::Fe32768::POLYNOMIAL: Self
+pub const bech32::primitives::gf32_ext::Fe32768::ZERO: Self
 pub const bech32::primitives::hrp::BC: bech32::primitives::hrp::Hrp
 pub const bech32::primitives::hrp::BCRT: bech32::primitives::hrp::Hrp
 pub const bech32::primitives::hrp::TB: bech32::primitives::hrp::Hrp
@@ -750,6 +776,14 @@ pub fn &bech32::primitives::gf32_ext::Fe1024::mul(self, other: &bech32::primitiv
 pub fn &bech32::primitives::gf32_ext::Fe1024::mul(self, other: bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
 pub fn &bech32::primitives::gf32_ext::Fe1024::sub(self, other: &bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
 pub fn &bech32::primitives::gf32_ext::Fe1024::sub(self, other: bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
+pub fn &bech32::primitives::gf32_ext::Fe32768::add(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::add(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::div(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::div(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::mul(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::mul(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::sub(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::sub(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
 pub fn &bech32::primitives::gf32_ext::Fe32Ext<DEG>::mul(self, other: &bech32::primitives::gf32::Fe32) -> Self::Output
 pub fn &bech32::primitives::gf32_ext::Fe32Ext<DEG>::mul(self, other: bech32::primitives::gf32::Fe32) -> Self::Output
 pub fn bech32::ByteIterExt::bytes_to_fes(self) -> bech32::primitives::iter::BytesToFes<Self>
@@ -971,6 +1005,20 @@ pub fn bech32::primitives::gf32_ext::Fe1024::mul_assign(&mut self, other: &bech3
 pub fn bech32::primitives::gf32_ext::Fe1024::multiplicative_inverse(self) -> Self
 pub fn bech32::primitives::gf32_ext::Fe1024::sub(self, other: &bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
 pub fn bech32::primitives::gf32_ext::Fe1024::sub_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe1024)
+pub fn bech32::primitives::gf32_ext::Fe32768::_add(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_div(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_mul(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_neg(self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_sub(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::add(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::add_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
+pub fn bech32::primitives::gf32_ext::Fe32768::div(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::div_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
+pub fn bech32::primitives::gf32_ext::Fe32768::mul(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::mul_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
+pub fn bech32::primitives::gf32_ext::Fe32768::multiplicative_inverse(self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::sub(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::sub_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
 pub fn bech32::primitives::gf32_ext::Fe32Ext<DEG>::clone(&self) -> bech32::primitives::gf32_ext::Fe32Ext<DEG>
 pub fn bech32::primitives::gf32_ext::Fe32Ext<DEG>::eq(&self, other: &bech32::primitives::gf32_ext::Fe32Ext<DEG>) -> bool
 pub fn bech32::primitives::gf32_ext::Fe32Ext<DEG>::fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result
@@ -1122,9 +1170,11 @@ pub trait bech32::primitives::iter::ByteIterExt: core::marker::Sized + core::ite
 pub trait bech32::primitives::iter::Fe32IterExt: core::marker::Sized + core::iter::traits::iterator::Iterator<Item = bech32::primitives::gf32::Fe32>
 pub type &bech32::primitives::gf32::Fe32::Output = bech32::primitives::gf32::Fe32
 pub type &bech32::primitives::gf32_ext::Fe1024::Output = bech32::primitives::gf32_ext::Fe32Ext<2>
+pub type &bech32::primitives::gf32_ext::Fe32768::Output = bech32::primitives::gf32_ext::Fe32Ext<3>
 pub type &bech32::primitives::gf32_ext::Fe32Ext<DEG>::Output = bech32::primitives::gf32_ext::Fe32Ext<DEG>
 pub type bech32::Checksum::MidstateRepr: bech32::primitives::checksum::PackedFe32
 pub type bech32::Fe1024 = bech32::primitives::gf32_ext::Fe32Ext<2>
+pub type bech32::Fe32768 = bech32::primitives::gf32_ext::Fe32Ext<3>
 pub type bech32::primitives::Bech32::MidstateRepr = u32
 pub type bech32::primitives::Bech32m::MidstateRepr = u32
 pub type bech32::primitives::ExtensionField::BaseField: bech32::primitives::Field
@@ -1143,6 +1193,9 @@ pub type bech32::primitives::gf32::Fe32::Output = bech32::primitives::gf32::Fe32
 pub type bech32::primitives::gf32_ext::Fe1024 = bech32::primitives::gf32_ext::Fe32Ext<2>
 pub type bech32::primitives::gf32_ext::Fe1024::BaseField = bech32::primitives::gf32::Fe32
 pub type bech32::primitives::gf32_ext::Fe1024::Output = bech32::primitives::gf32_ext::Fe32Ext<2>
+pub type bech32::primitives::gf32_ext::Fe32768 = bech32::primitives::gf32_ext::Fe32Ext<3>
+pub type bech32::primitives::gf32_ext::Fe32768::BaseField = bech32::primitives::gf32::Fe32
+pub type bech32::primitives::gf32_ext::Fe32768::Output = bech32::primitives::gf32_ext::Fe32Ext<3>
 pub type bech32::primitives::gf32_ext::Fe32Ext<DEG>::Output = bech32::primitives::gf32_ext::Fe32Ext<DEG>
 pub type bech32::primitives::hrp::ByteIter<'b>::Item = u8
 pub type bech32::primitives::hrp::CharIter<'b>::Item = char
diff --git a/api/no-features.txt b/api/no-features.txt
index 74b0f119d..4357094c9 100644
--- a/api/no-features.txt
+++ b/api/no-features.txt
@@ -15,8 +15,10 @@
 #[repr(transparent)] pub struct bech32::Fe32(_)
 #[repr(transparent)] pub struct bech32::primitives::gf32::Fe32(_)
 impl bech32::primitives::ExtensionField for bech32::primitives::gf32_ext::Fe1024
+impl bech32::primitives::ExtensionField for bech32::primitives::gf32_ext::Fe32768
 impl bech32::primitives::Field for bech32::primitives::gf32::Fe32
 impl bech32::primitives::Field for bech32::primitives::gf32_ext::Fe1024
+impl bech32::primitives::Field for bech32::primitives::gf32_ext::Fe32768
 impl bech32::primitives::checksum::Checksum for bech32::primitives::Bech32
 impl bech32::primitives::checksum::Checksum for bech32::primitives::Bech32m
 impl bech32::primitives::checksum::Checksum for bech32::primitives::NoChecksum
@@ -269,42 +271,58 @@ impl core::ops::arith::Add<&bech32::primitives::gf32::Fe32> for &bech32::primiti
 impl core::ops::arith::Add<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Add<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Add<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Add<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Add<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::AddAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::AddAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::AddAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::AddAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Div for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<&bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Div<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Div<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Div<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Div<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::DivAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::DivAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::DivAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::DivAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Mul for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<&bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Mul<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Mul<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Mul<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Mul<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::MulAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::MulAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::MulAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::MulAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Neg for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<&bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
 impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
+impl core::ops::arith::Sub<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::Sub<bech32::primitives::gf32::Fe32> for &bech32::primitives::gf32::Fe32
 impl core::ops::arith::Sub<bech32::primitives::gf32_ext::Fe32Ext<2>> for &bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::Sub<bech32::primitives::gf32_ext::Fe32Ext<3>> for &bech32::primitives::gf32_ext::Fe32768
 impl core::ops::arith::SubAssign for bech32::primitives::gf32::Fe32
 impl core::ops::arith::SubAssign<&bech32::primitives::gf32::Fe32> for bech32::primitives::gf32::Fe32
 impl core::ops::arith::SubAssign<&bech32::primitives::gf32_ext::Fe32Ext<2>> for bech32::primitives::gf32_ext::Fe1024
+impl core::ops::arith::SubAssign<&bech32::primitives::gf32_ext::Fe32Ext<3>> for bech32::primitives::gf32_ext::Fe32768
 impl core::ops::bit::BitXor for bech32::primitives::checksum::PackedNull
 impl core::panic::unwind_safe::RefUnwindSafe for bech32::EncodeError
 impl core::panic::unwind_safe::RefUnwindSafe for bech32::primitives::Bech32
@@ -664,6 +682,14 @@ pub const bech32::primitives::gf32_ext::Fe1024::MULTIPLICATIVE_ORDER_FACTORS: &'
 pub const bech32::primitives::gf32_ext::Fe1024::ONE: Self
 pub const bech32::primitives::gf32_ext::Fe1024::POLYNOMIAL: Self
 pub const bech32::primitives::gf32_ext::Fe1024::ZERO: Self
+pub const bech32::primitives::gf32_ext::Fe32768::DEGREE: usize
+pub const bech32::primitives::gf32_ext::Fe32768::EXT_ELEM: Self
+pub const bech32::primitives::gf32_ext::Fe32768::GENERATOR: Self
+pub const bech32::primitives::gf32_ext::Fe32768::MULTIPLICATIVE_ORDER: usize
+pub const bech32::primitives::gf32_ext::Fe32768::MULTIPLICATIVE_ORDER_FACTORS: &'static [usize]
+pub const bech32::primitives::gf32_ext::Fe32768::ONE: Self
+pub const bech32::primitives::gf32_ext::Fe32768::POLYNOMIAL: Self
+pub const bech32::primitives::gf32_ext::Fe32768::ZERO: Self
 pub const bech32::primitives::hrp::BC: bech32::primitives::hrp::Hrp
 pub const bech32::primitives::hrp::BCRT: bech32::primitives::hrp::Hrp
 pub const bech32::primitives::hrp::TB: bech32::primitives::hrp::Hrp
@@ -699,6 +725,14 @@ pub fn &bech32::primitives::gf32_ext::Fe1024::mul(self, other: &bech32::primitiv
 pub fn &bech32::primitives::gf32_ext::Fe1024::mul(self, other: bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
 pub fn &bech32::primitives::gf32_ext::Fe1024::sub(self, other: &bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
 pub fn &bech32::primitives::gf32_ext::Fe1024::sub(self, other: bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
+pub fn &bech32::primitives::gf32_ext::Fe32768::add(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::add(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::div(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::div(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::mul(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::mul(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::sub(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn &bech32::primitives::gf32_ext::Fe32768::sub(self, other: bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
 pub fn &bech32::primitives::gf32_ext::Fe32Ext<DEG>::mul(self, other: &bech32::primitives::gf32::Fe32) -> Self::Output
 pub fn &bech32::primitives::gf32_ext::Fe32Ext<DEG>::mul(self, other: bech32::primitives::gf32::Fe32) -> Self::Output
 pub fn bech32::ByteIterExt::bytes_to_fes(self) -> bech32::primitives::iter::BytesToFes<Self>
@@ -912,6 +946,20 @@ pub fn bech32::primitives::gf32_ext::Fe1024::mul_assign(&mut self, other: &bech3
 pub fn bech32::primitives::gf32_ext::Fe1024::multiplicative_inverse(self) -> Self
 pub fn bech32::primitives::gf32_ext::Fe1024::sub(self, other: &bech32::primitives::gf32_ext::Fe1024) -> bech32::primitives::gf32_ext::Fe1024
 pub fn bech32::primitives::gf32_ext::Fe1024::sub_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe1024)
+pub fn bech32::primitives::gf32_ext::Fe32768::_add(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_div(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_mul(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_neg(self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::_sub(&self, other: &Self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::add(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::add_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
+pub fn bech32::primitives::gf32_ext::Fe32768::div(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::div_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
+pub fn bech32::primitives::gf32_ext::Fe32768::mul(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::mul_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
+pub fn bech32::primitives::gf32_ext::Fe32768::multiplicative_inverse(self) -> Self
+pub fn bech32::primitives::gf32_ext::Fe32768::sub(self, other: &bech32::primitives::gf32_ext::Fe32768) -> bech32::primitives::gf32_ext::Fe32768
+pub fn bech32::primitives::gf32_ext::Fe32768::sub_assign(&mut self, other: &bech32::primitives::gf32_ext::Fe32768)
 pub fn bech32::primitives::gf32_ext::Fe32Ext<DEG>::clone(&self) -> bech32::primitives::gf32_ext::Fe32Ext<DEG>
 pub fn bech32::primitives::gf32_ext::Fe32Ext<DEG>::eq(&self, other: &bech32::primitives::gf32_ext::Fe32Ext<DEG>) -> bool
 pub fn bech32::primitives::gf32_ext::Fe32Ext<DEG>::fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result
@@ -1047,9 +1095,11 @@ pub trait bech32::primitives::iter::ByteIterExt: core::marker::Sized + core::ite
 pub trait bech32::primitives::iter::Fe32IterExt: core::marker::Sized + core::iter::traits::iterator::Iterator<Item = bech32::primitives::gf32::Fe32>
 pub type &bech32::primitives::gf32::Fe32::Output = bech32::primitives::gf32::Fe32
 pub type &bech32::primitives::gf32_ext::Fe1024::Output = bech32::primitives::gf32_ext::Fe32Ext<2>
+pub type &bech32::primitives::gf32_ext::Fe32768::Output = bech32::primitives::gf32_ext::Fe32Ext<3>
 pub type &bech32::primitives::gf32_ext::Fe32Ext<DEG>::Output = bech32::primitives::gf32_ext::Fe32Ext<DEG>
 pub type bech32::Checksum::MidstateRepr: bech32::primitives::checksum::PackedFe32
 pub type bech32::Fe1024 = bech32::primitives::gf32_ext::Fe32Ext<2>
+pub type bech32::Fe32768 = bech32::primitives::gf32_ext::Fe32Ext<3>
 pub type bech32::primitives::Bech32::MidstateRepr = u32
 pub type bech32::primitives::Bech32m::MidstateRepr = u32
 pub type bech32::primitives::ExtensionField::BaseField: bech32::primitives::Field
@@ -1068,6 +1118,9 @@ pub type bech32::primitives::gf32::Fe32::Output = bech32::primitives::gf32::Fe32
 pub type bech32::primitives::gf32_ext::Fe1024 = bech32::primitives::gf32_ext::Fe32Ext<2>
 pub type bech32::primitives::gf32_ext::Fe1024::BaseField = bech32::primitives::gf32::Fe32
 pub type bech32::primitives::gf32_ext::Fe1024::Output = bech32::primitives::gf32_ext::Fe32Ext<2>
+pub type bech32::primitives::gf32_ext::Fe32768 = bech32::primitives::gf32_ext::Fe32Ext<3>
+pub type bech32::primitives::gf32_ext::Fe32768::BaseField = bech32::primitives::gf32::Fe32
+pub type bech32::primitives::gf32_ext::Fe32768::Output = bech32::primitives::gf32_ext::Fe32Ext<3>
 pub type bech32::primitives::gf32_ext::Fe32Ext<DEG>::Output = bech32::primitives::gf32_ext::Fe32Ext<DEG>
 pub type bech32::primitives::hrp::ByteIter<'b>::Item = u8
 pub type bech32::primitives::hrp::CharIter<'b>::Item = char
diff --git a/src/lib.rs b/src/lib.rs
index ab86aeb21..4ca1381b1 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -161,7 +161,7 @@ use crate::primitives::decode::{ChecksumError, UncheckedHrpstring, UncheckedHrps
 pub use {
     crate::primitives::checksum::Checksum,
     crate::primitives::gf32::Fe32,
-    crate::primitives::gf32_ext::Fe1024,
+    crate::primitives::gf32_ext::{Fe1024, Fe32768},
     crate::primitives::hrp::Hrp,
     crate::primitives::iter::{ByteIterExt, Fe32IterExt},
     crate::primitives::{Bech32, Bech32m, NoChecksum},
diff --git a/src/primitives/gf32_ext.rs b/src/primitives/gf32_ext.rs
index 5fddebed8..faff434b1 100644
--- a/src/primitives/gf32_ext.rs
+++ b/src/primitives/gf32_ext.rs
@@ -183,6 +183,95 @@ impl ExtensionField for Fe1024 {
     const EXT_ELEM: Self = Self::new([Fe32::Q, Fe32::P]);
 }
 
+/// The field of order 32768.
+pub type Fe32768 = Fe32Ext<3>;
+
+impl Field for Fe32768 {
+    /// The zero element of the field.
+    const ZERO: Self = Self::new([Fe32::Q, Fe32::Q, Fe32::Q]);
+
+    /// The one element of the field.
+    const ONE: Self = Self::new([Fe32::P, Fe32::Q, Fe32::Q]);
+
+    // Chosen somewhat arbitrarily, by just guessing values until one came
+    // out with the correct order.
+    /// A generator of the field.
+    const GENERATOR: Self = Self::new([Fe32::A, Fe32::C, Fe32::Q]);
+
+    /// The order of the multiplicative group of the field.
+    ///
+    /// This constant also serves as a compile-time check that we can count
+    /// the entire field using a `usize` as a counter.
+    const MULTIPLICATIVE_ORDER: usize = 32767;
+
+    const MULTIPLICATIVE_ORDER_FACTORS: &'static [usize] = &[1, 7, 31, 151, 217, 1057, 4681, 32767];
+
+    #[inline]
+    fn _add(&self, other: &Self) -> Self {
+        Self::new([
+            self.inner[0] + other.inner[0],
+            self.inner[1] + other.inner[1],
+            self.inner[2] + other.inner[2],
+        ])
+    }
+
+    #[inline]
+    fn _sub(&self, other: &Self) -> Self { self._add(other) }
+
+    #[inline]
+    fn _mul(&self, other: &Self) -> Self { self.mul_by_elem(other) }
+
+    #[inline]
+    fn _div(&self, other: &Self) -> Self { other.multiplicative_inverse() * self }
+
+    #[inline]
+    fn _neg(self) -> Self { self }
+
+    fn multiplicative_inverse(self) -> Self {
+        // Unlike in the GF1024 case we don't bother being generic over
+        // arbitrary values of POLYNOMIAL, since doing so means a ton
+        // of extra work for everybody (me, the reviewer, and the CPU
+        // that has to do a bunch of mulitplications by values that
+        // turn out to always be 0).
+        debug_assert_eq!(Self::POLYNOMIAL, Self::new([Fe32::P, Fe32::P, Fe32::Q]));
+        // Aliases to make the below equations easier to read
+        let a0 = self.inner[0];
+        let a1 = self.inner[1];
+        let a2 = self.inner[2];
+
+        let a0_2 = a0 * a0;
+        let a1_2 = a1 * a1;
+        let a2_2 = a2 * a2;
+
+        let a0a1 = a0 * a1;
+        let a0a2 = a0 * a2;
+        let a1a2 = a1 * a2;
+
+        // Inverse of the 3x3 multiplication matrix defined by a0, a1, a2.
+        let det = (a0_2 * a0) + a1_2 * (a0 + a1) + a2_2 * (a0 + a1 + a2) + (a0 * a1a2);
+        Self::new([
+            (a0_2 + a1_2 + a2_2 + a1a2) / det,
+            (a2_2 + a0a1) / det,
+            (a1_2 + a2_2 + a0a2) / det,
+        ])
+    }
+}
+super::impl_ops_for_fe!(impl for Fe32768);
+
+impl ExtensionField for Fe32768 {
+    type BaseField = Fe32;
+
+    const DEGREE: usize = 3;
+
+    // Arbitrary irreducible polynomial x^3 = x + 1
+    const POLYNOMIAL: Self = Self::new([Fe32::P, Fe32::P, Fe32::Q]);
+
+    /// The element zeta such that the extension field is defined as `GF32[zeta]`.
+    ///
+    /// Alternately, the image of x in the mapping `GF32[x]/p(x) -> <the field>`
+    const EXT_ELEM: Self = Self::new([Fe32::Q, Fe32::P, Fe32::Q]);
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -269,4 +358,37 @@ mod tests {
         assert_eq!(elem.powi(3).multiplicative_order(), 341);
         assert_eq!(elem.powi(341).multiplicative_order(), 3);
     }
+
+    #[test]
+    fn gf32768_mult_inverse() {
+        assert_eq!(Fe32768::ONE.multiplicative_inverse(), Fe32768::ONE);
+
+        for i in 0..32 {
+            for j in 0..32 {
+                for k in 0..32 {
+                    if i != 0 || j != 0 || k != 0 {
+                        let fe32768 = Fe32768::new([Fe32(i), Fe32(j), Fe32(k)]);
+                        assert_eq!(
+                            fe32768.multiplicative_inverse().multiplicative_inverse(),
+                            fe32768,
+                        );
+                    }
+                }
+            }
+        }
+    }
+
+    #[test]
+    fn gf32768_powi() {
+        // A "random" element
+        let elem = Fe32768::new([Fe32::A, Fe32::C, Fe32::Q]);
+        assert_eq!(elem.powi(2), elem * elem);
+        assert_eq!(elem.powi(3), elem * elem * elem);
+        assert_eq!(elem.powi(0), Fe32768::ONE);
+        assert_eq!(elem.powi(-1), elem.multiplicative_inverse());
+
+        assert_eq!(elem.multiplicative_order(), 32767);
+        assert_eq!(elem.powi(7).multiplicative_order(), 4681);
+        assert_eq!(elem.powi(341).multiplicative_order(), 1057);
+    }
 }