Related papers: DNA codes over two noncommutative rings of order f…
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…
An important class of codes widely used in applications is the class of convolutional codes. Most of the literature of convolutional codes is devoted to con- volutional codes over finite fields. The extension of the concept of convolutional…
A Type IV-II Z4-code is a self-dual code over Z4 with the property that all Euclidean weights are divisible by eight and all codewords have even Hamming weight. In this paper we use generalized bent functions for a construction of…
In this paper, we consider the problem of designing DNA sequences (codewords) for DNA storage systems and DNA computing that are unlikely to fold back onto themselves to form undesirable secondary structures. The paper addresses both the…
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…
In this work, four circulant and quadratic double circulant (QDC) constructions are applied to the family of the rings R_k,m. Self-dual binary codes are obtained as the Gray images of self-dual QDC codes over R_k,m. Extremal binary…
Let $R$ be a finite commutative chain ring with unique maximal ideal $\langle \gamma\rangle$, and let $n$ be a positive integer coprime with the characteristic of $R/\langle \gamma\rangle$. In this paper, the algebraic structure of cyclic…
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 \lambda-circulant and \lambda-reverse circulant matrices. By using the constructions on…
In this work, quadratic reside codes over the ring F2 +uF2 +u^2F2 with u^3 = u are considered. A duality and distance preserving Gray map from F2 + uF2 + u^2F2 to (F_2)^3 is defined. By using quadratic double circulant, quadratic bordered…
While achieving a compression ratio of 2.0 bits/base, the new algorithm codes non-N bases in fixed length. It dramatically reduces the time of coding and decoding than previous DNA compression algorithms and some universal compression…
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…
Double circulant codes of length $2n$ over the semilocal ring $R = \mathbb{F}_q + u\mathbb{F}_q,\, u^2=u,$ are studied when $q$ is an odd prime power, and $-1$ is a square in $\mathbb{F}_q.$ Double negacirculant codes of length $2n$ are…
Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algorithm for factorizing $x^n-\lambda$ over $\mathbb{F}_{q^2}$ is given, where $\lambda$ is a unit in $\mathbb{F}_{q^2}$. Based on this…
We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a…
In this paper, we study self-dual codes over $\mathbb{Z}_2 \times (\mathbb{Z}_2+u\mathbb{Z}_2) $, where $u^2=0$. Three types of self-dual codes are defined. For each type, the possible values $\alpha,\beta$ such that there exists a code…
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…
In this paper, we introduce a new definitions of the Gray weight and the Gray map for linear codes over $\mathbb{Z}_9+u\mathbb{Z}_9$ with $u^2=u$. Some results on self-dual codes over this ring are investigated. Further, the structural…
In this work, we define a modification of a bordered construction for self-dual codes which utilises $\lambda$-circulant matrices. We provide the necessary conditions for the construction to produce self-dual codes over finite commutative…
Let $\mathbb{F}_{q}$ be a finite field of cardinality $q$, $R=\mathbb{F}_{q}[u]/\langle u^4\rangle=\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}+u^3\mathbb{F}_{q}$ $(u^4=0)$ which is a finite chain ring, and $n$ be a positive integer…
We study the primary DNA structure of four of the most completely sequenced human chromosomes (including chromosome 19 which is the most dense in coding), using Non-extensive Statistics. We show that the exponents governing the decay of the…