Related papers: Construction of Quasi-Cyclic Product Codes
In this paper, we study the structure of 1-generator quasi-cyclic codes over the ring R = F2 + uF2 + vF2 + uvF2, with u2 = v2 = 0 and uv = vu. We determine the minimal spanning sets for these codes. As a generalization of these codes, we…
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…
Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the…
Based on cyclic simplex codes, a new construction of a family of 2-generator quasi-cyclic two-weight codes is given. New optimal binary quasi-cyclic [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, good QC ternary [195, 6, 126], [208,…
We study complementary information set codes of length $tn$ and dimension $n$ of order $t$ called ($t-$CIS code for short). Quasi-cyclic and quasi-twisted $t$-CIS codes are enumerated by using their concatenated structure. Asymptotic…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
The aim of this paper is to determine the algebraic structure of multidimensional cyclic codes over a finite chain ring $\mathfrak{R}$. An algorithm to find the generator polynomials of $n$ dimensional ($n$D) cyclic codes of length…
One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the…
LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are…
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in…
The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic…
In this paper we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a non-commutative ring called the skew polynomial rings $F[x;\theta ]$. After a brief description of the skew…
A binary linear code $C$ is a $\mathbb{Z}_2$-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be…
Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on…
This paper consists of three parts. The first part presents a large class of new binary quasi-cyclic (QC)-LDPC codes with girth of at least 6 whose parity-check matrices are constructed based on cyclic subgroups of finite fields.…
Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that…
A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the…
Many classical constructions, such as Plotkin's and Turyn's, were generalized by matrix product (MP) codes. Quasi-twisted (QT) codes, on the other hand, form an algebraically rich structure class that contains many codes with best-known…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
We introduce the first example of algebraically constructed hierarchical quasi-cyclic codes. These codes are built from Reed-Solomon codes using a 1964 construction of superimposed codes by Kautz and Singleton. We show both the number of…