diff --git a/backend/src/encoding.rs b/backend/src/encoding.rs
index 55bba09..27d4b8c 100644
--- a/backend/src/encoding.rs
+++ b/backend/src/encoding.rs
@@ -269,12 +269,12 @@ fn decode_coeff_i64<D: AsRef<[u8]>>(a: &VecZnx<D>, col_i: usize, basek: usize, k
 
     let size: usize = (k + basek - 1) / basek;
     let data: &[i64] = a.raw();
-    let mut res: i64 = data[i];
+    let mut res: i64 = 0;
     let rem: usize = basek - (k % basek);
     let slice_size: usize = a.n() * a.cols();
-    (0..size).for_each(|i| {
-        let x: i64 = data[i * slice_size];
-        if i == size - 1 && rem != basek {
+    (0..size).for_each(|j| {
+        let x: i64 = data[j * slice_size + i];
+        if j == size - 1 && rem != basek {
             let k_rem: usize = basek - rem;
             res = (res << k_rem) + (x >> rem);
         } else {
@@ -320,7 +320,7 @@ mod tests {
         let module: Module<FFT64> = Module::<FFT64>::new(n);
         let basek: usize = 17;
         let size: usize = 5;
-        for k in [size * basek - 5] {
+        for k in [1, basek / 2, size * basek - 5] {
             let mut a: VecZnx<_> = module.new_vec_znx(2, size);
             let mut source = Source::new([0u8; 32]);
             let raw: &mut [i64] = a.raw_mut();
diff --git a/core/src/glwe/external_product.rs b/core/src/glwe/external_product.rs
index 3ebf339..3f826f1 100644
--- a/core/src/glwe/external_product.rs
+++ b/core/src/glwe/external_product.rs
@@ -18,7 +18,7 @@ impl GLWECiphertext<Vec<u8>> {
         let in_size: usize = k_in.div_ceil(basek).div_ceil(digits);
         let out_size: usize = k_out.div_ceil(basek);
         let ggsw_size: usize = k_ggsw.div_ceil(basek);
-        let vmp: usize = module.bytes_of_vec_znx_dft(rank + 1, in_size)
+        let vmp: usize = module.bytes_of_vec_znx_dft(rank + 1, ggsw_size)
             + module.vmp_apply_tmp_bytes(
                 out_size,
                 in_size,
diff --git a/core/src/glwe/ops.rs b/core/src/glwe/ops.rs
index 2beffe6..d921583 100644
--- a/core/src/glwe/ops.rs
+++ b/core/src/glwe/ops.rs
@@ -14,6 +14,7 @@ pub trait GLWEOps: GLWECiphertextToMut + Infos + SetMetaData {
             assert_eq!(b.n(), module.n());
             assert_eq!(self.n(), module.n());
             assert_eq!(a.basek(), b.basek());
+            assert_eq!(self.basek(), a.basek());
             assert!(self.rank() >= a.rank().max(b.rank()));
         }
 
@@ -46,8 +47,8 @@ pub trait GLWEOps: GLWECiphertextToMut + Infos + SetMetaData {
             });
         });
 
-        self.set_basek(a.basek());
-        self.set_k(a.k().max(b.k()));
+        // self.set_basek(a.basek());
+        // self.set_k(a.k().max(b.k()));
     }
 
     fn add_inplace<A>(&mut self, module: &Module<FFT64>, a: &A)
diff --git a/core/src/lib.rs b/core/src/lib.rs
index ba28589..eb3cbce 100644
--- a/core/src/lib.rs
+++ b/core/src/lib.rs
@@ -19,6 +19,7 @@ pub use glwe::{GLWECiphertext, GLWEOps, GLWEPacker, GLWEPlaintext, GLWEPublicKey
 pub(crate) use glwe::{GLWECiphertextToMut, GLWECiphertextToRef};
 pub use lwe::{LWECiphertext, LWESecret};
 
+pub use backend;
 pub use backend::Scratch;
 pub use backend::ScratchOwned;