Related papers: Z2Z4Z8-Cyclic Codes
Additive cyclic codes over Galois rings were investigated in previous works. In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative…
In this paper, we study the codes over the matrix ring over $\mathbb{Z}_4$, which is perhaps the first time the ring structure $M_2(\mathbb{Z}_4)$ is considered as a code alphabet. This ring is isomorphic to…
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain…
Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over $\mathbb{Z}_4$ including the normalized generating…
In this paper, we count the number of matrices whose rows generate different $\mathbb{Z}_2\mathbb{Z}_8$ additive codes. This is a natural generalization of the well known Gaussian numbers that count the number of matrices whose rows…
Let $R=\mathbb{Z}_4$ be the integer ring mod $4$. A double cyclic code of length $(r,s)$ over $R$ is a set that can be partitioned into two parts that any cyclic shift of the coordinates of both parts leaves invariant the code. These codes…
Let $\mathbb{F}_{q}$ be the finite field with $q$ elements. This paper mainly researches the polynomial representation of double cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^2\mathbb{F}_{q}$ with $v^3=v$. Firstly, we give the…
We construct a class of $\mathbb{Z}_2\mathbb{Z}_4$-additive cyclic codes generated by pairs of polynomials, study their algebraic structures, and obtain the generator matrix of any code in the class. Using a probabilistic method, we prove…
In this paper, we have studied cyclic codes over the ring $R=\mathbb{Z}_4+u\mathbb{Z}_4$, $u^2=0$. We have considered cyclic codes of odd lengths. A sufficient condition for a cyclic code over $R$ to be a $\mathbb{Z}_4$-free module is…
The rings $Z_{4}+\nu Z_{4}$ have been classified into chain rings and non-chain rings on the basis of the values of $\nu^{2} \in Z_{4}+\nu Z_{4}.$ In this paper, the structure of cyclic codes of arbitrary length over the rings $Z_{4}+\nu…
Quasi-cyclic (QC) codes form an important generalization of cyclic codes. It is well know that QC codes of length $s\ell$ with index $s$ over the finite field $\mathbb{F}$ are $\mathbb{F}[y]$-submodules of the ring $\frac{\mathbb{F}[x,y]}{<…
In this study, in order to get better codes, we focus on double skew cyclic codes over the ring $\mathrm{R}= \mathbb{F}_q+v\mathbb{F}_q, ~v^2=v$ where $q$ is a prime power. We investigate the generator polynomials, minimal spanning sets,…
The purpose of this paper is to study the cyclic self orthogonal codes over $\mathbb{Z}_{p^m}$. After providing the generator polynomial of cyclic self orthogonal codes over $\mathbb{Z}_{p^m}$, we give the necessary and sufficient condition…
In this paper, we study the theory for constructing DNA cyclic codes of odd length over $\Z_4[u]/\langle u^2 \rangle$ which play an important role in DNA computing. Cyclic codes of odd length over $\Z_4 + u \Z_4$ satisfy the reverse…
The permutation groups of cyclic codes are widely applicable in determining the weight distribution of codes, decoding theory and various other areas. In this paper, by employing two distinct matrix representations, we can relate cyclic…
A Z2Z4Q8-code is a non-empty subgroup of a direct product of copies of Z_2, Z_4 and Q_8 (the binary field, the ring of integers modulo 4 and the quaternion group on eight elements, respectively). Such Z2Z4Q8-codes are translation invariant…
Let $\mathbb{Z}_{p}$ be the ring of residue classes modulo a prime $p$. The $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive cyclic codes of length $(\alpha,\beta)$ is identify as $\mathbb{Z}_{p}[u,v][x]$-submodule of $\mathbb{Z}_{p}[x]/\langle…
Zipper codes are a framework for describing spatially-coupled product-like codes. Many well-known codes, such as staircase codes and braided block codes, are subsumed into this framework. New types of codes such as tiled diagonal and…
We study one generator quasi-cyclic codes and four-circulant codes, which are also quasi-cyclic but have two generators. We state the hull dimensions for both classes of codes in terms of the polynomials in their generating elements. We…
This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are…