Related papers: The permutation automorphism groups of irreducible…
An $f$-subgroup is a linear recurring sequence subgroup, a multiplicative subgroup of a field whose elements can be generated (without repetition) by a linear recurrence relation, with characteristic polynomial $f$. It is called…
An important family of codes for data storage systems, cryptography, consumer electronics, and network coding for error control in digital communications are the so-called cyclic codes. This kind of linear codes are also important due to…
In this paper, we construct a special family of cyclic codes, known as quadratic residue codes of prime length \( p \equiv \pm 1 \pmod{44} ,\) \( p \equiv \pm 5 \pmod{44} ,\) \( p \equiv \pm 7 \pmod{44} ,\) \( p \equiv \pm 9 \pmod{44} \)…
The automorphism group of a code is the group of permutations that map a code to itself. Berman codes are a class of binary linear codes characterized by two integer parameters $n\geq 2$ and $m\geq 1$, and this class includes the…
A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism from FG to Fn which maps G to the standard basis of Fn. Many classical linear codes have been shown to be group…
Let $G$ be a finite abelian group. Ferraz, Guerreiro and Polcino Milies prove that the number of $G$-equivalence classes of minimal abelian codes is equal to the number of $G$-isomorphism classes of subgroups for which corresponding…
The completely regular codes in Hamming graphs have a high degree of combinatorial symmetry and have attracted a lot of interest since their introduction in 1973 by Delsarte. This paper studies the subfamily of completely transitive codes,…
This article begins with an exploration of nonlinear codes ($\mathbb{F}_q$-linear subspaces of $\mathbb{F}_{q^m}^n$) which are generalizations of the familiar Reed-Solomon codes. This then leads to a wider exploration of nonlinear analogues…
In order to complete (and generalize) results of Gardiner and Praeger on 4-valent symmetric graphs (European J. Combin, 15 (1994)) we apply the method of lifting automorphisms in the context of elementary-abelian covering projections. In…
In this paper, the cyclic codes of length $n$, where $n$ is odd with certain restrictions, over a finite chain ring $R$, have been studied using the structure of group algebra approach. The primitive idempotents of $RG$ of a finite cyclic…
Interplay between coding theory and combinatorial $t$-designs has been a hot topic for many years for combinatorialists and coding theorists. Some infinite families of cyclic codes supporting infinite families of $3$-designs have been…
In this article, we study skew cyclic codes over ring $R=\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and $v^{3}=v$. We describe generator polynomials of skew cyclic codes over this ring and…
Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\theta : \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. In this paper, we deal with skew constacyclic codes, that is, linear codes of $\mathbb{F}_q^n$…
Let C be an arbitrary simple-root cyclic code and let G be the subgroup of Aut(C) (the automorphism group of C) generated by the multiplier, the cyclic shift and the scalar multiplications. To the best of our knowledge, the subgroup G is…
We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for…
In coding theory, a very interesting problem (but at the same time, a very difficult one) is to determine the weight distribution of a given code. This problem is even more interesting for cyclic codes, and this is so, mainly because they…
We propose a simple criterion to know if an abelian variety $A$ defined over a finite field $\mathbb{F}_q$ is cyclic, i.e., it has a cyclic group of rational points; this criterion is based on the endomorphism ring End$_{\mathbb{F}_q}(A)$.…
Irreducible cyclic codes are one of the largest known classes of block codes which have been investigated for a long time. However, their weight distributions are known only for a few cases. In this paper, a class of irreducible cyclic…
In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field $F=\mathbb{F}_q$. We obtain the generator matrices and generator polynomials of these codes and their duals. We also investigate…
We investigate the properties of binary linear codes of even length whose permutation automorphism group is a cyclic group generated by an involution. Up to dimension or co-dimension $4$, we show that there is no quasi group code whose…