In this work, we establish a strong connection between group rings and self-dual codes. We
prove that a group ring element corresponds to a self-dual code if and only if it is a unitary …

In this work, we propose a modified four circulant construction for self-dual codes and a
bordered version of the construction using the properties of λ-circulant and λ-reverse …

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 …

Abstract Recently, Karadeniz and Yildiz introduced an efficient method to search for self-
dual codes. It is called lifting method and can be applied to some alphabets. In this work, by …

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 work, we present a new method for constructing self-dual codes over finite
commutative rings R with characteristic 2. Our method involves searching for k× 2 k matrices …

A lift of binary self-dual codes to the ring R< sub> 2 is described. By using this lift, a family of
self-dual codes over R< sub> 2 of length 17 are constructed. Taking the binary images of …

In this work, we provide a variation of the four-circulant construction for selfdual codes. By
applying the constructions over the alphabets F2, F2+ uF2, F4+ uF4, we were able to obtain …

In this paper, we give a method to lift binary self-dual codes to the ring R k. The lifting
method requires solving a system of linear equations over R k. This technique is applied to …

We define a class of finite Frobenius rings of order 2 2 k, describe their generating
characters, and study codes over these rings. We define two conjugate weight preserving …