Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

We prove that self-dual codes exist over all finite commutative Frobenius rings, via their
decomposition by the Chinese Remainder Theorem into local rings. We construct non-free …

Codes over an infinite family of rings which are an extension of the binary field are defined.
Two Gray maps to the binary field are attached and are shown to be conjugate. Euclidean …

This paper is dealing with DNA cyclic codes which play an important role in DNA computing
and have attracted a particular attention in the literature. Firstly, we introduce a new family of …

By using linear algebra over finite commutative rings, we will present some judging
criterions for linear complementary dual (LCD) codes over rings, in particular, free LCD …

We study codes over Frobenius rings. We describe Frobenius rings via an isomorphism to
the product of local Frobenius rings and use this decomposition to describe an analog of …

In this work, we first prove a necessary and sufficient condition for a pairs of linear codes
over finite rings to be linear complementary pairs (abbreviated to LCPs). In particular, a …

In this paper we give the structure of constacyclic codes over formal power series and chain
rings. We also present necessary and sufficient conditions on the existence of MDS codes …

We study self-dual codes over chain rings. We describe a technique for constructing new
self-dual codes from existing codes and we prove that for chain rings containing an element …

Abstract A pair (C, D) of group codes in R [G] is called a linear complementary pair
(abbreviated to LCP) if C⊕ D= R [G], where R is a finite Frobenius ring, and G is a finite …