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 …

Let F 2 m be a finite field of cardinality 2 m, R= F 2 m+ u F 2 m (u 2= 0) and s, n be positive
integers such that n is odd. In this paper, we give an explicit representation for every self …

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 …

We describe a composite construction from group rings where the groups have orders 16
and 8. This construction is then applied to find the extremal binary self-dual codes with …

In this work, extension theorems are used for self-dual codes over rings and as applications
many new binary self-dual extremal codes are found from self-dual codes over F 2 m+ u F 2 …

Let F 2 (m) be a finite field of 2 m elements, λ and k be integers satisfying λ, k≥ 2 and denote
R= F 2 (m)[u]/(u 2λ). Let δ, α∈ F 2 (m)×. For any odd positive integer n, we give an explicit …

In this work, quadratic double and quadratic bordered double circulant constructions are
applied to F 4+ u F 4 as well as to F 4, and as a result, extremal binary self-dual codes of …

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 …

In this work, we focus on constructing binary self-dual [68, 34, 12] and [88, 44, 14] codes with
new parameters in their weight enumerators. For this purpose, we present a new bordered …

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 …