In this work,(1+ v)-constacyclic codes over the ring F2+ uF2+ vF2+ uvF2 are studied.(1+ v)-
constacyclic codes over F2+ uF2+ vF2+ uvF2 of odd lengths are characterized with the help …

The study of linear codes over local rings, particularly non-chain rings, imposes difficulties
that differ from those encountered in codes over chain rings, and this stems from the fact that …

A classification of all four-circulant extremal codes of length 32 over 𝔽₂+ 𝑢𝔽₂ is done by
using four-circulant binary self-dual codes of length 32 of minimum weights 6 and 8. As Gray …

We study self-dual codes over non-commutative Frobenius rings. It is shown that a code is
equal to its left orthogonal if and only if it is equal to its right orthogonal. Constructions of self …

Constacyclic codes are an important class of linear codes in coding theory. Many optimal
linear codes are directly derived from constacyclic codes. In this paper,(1+ u)-constacyclic …

We obtain extremal binary self-dual codes of parameters [64, 32, 12] as binary images of self-
dual codes over R 1, R 2 and R 3 by employing different methods. We then apply the …

In this study we consider Euclidean and Hermitian self-dual codes over the direct product
ring F 2×(F 2+ v F 2) F_2*(F_2+vF_2) where v 2= v. We obtain some theoretical outcomes …

In this paper, we use the graded ring construction to lift the extended binary Hamming code
of length 8 to R_k R k. Using this method we construct self-dual codes over R_3 R 3 of …

In this work, we study codes over the ring 𝓡 k, m= 𝔽2 [u, v]/< uk, vm, uv− vu>, which is a
family of Frobenius, characteristic 2 extensions of the binary field. We introduce a distance …

In this work, the double-circulant, bordered-double-circulant and stripped bordered-double-
circulant constructions for self-dual codes over the non-chain ring R< sub> 2= F< sub> 2+ …