相关论文: Linear Codes over Z_4+uZ_4: MacWilliams identities…
It is known that a linear two-weight code $C$ over a finite field $\F_q$ corresponds both to a multiset in a projective space over $\F_q$ that meets every hyperplane in either $a$ or $b$ points for some integers $a<b$, and to a strongly…
For odd length $n$, the cyclic codes construction over $\Re= \Z_4[v]/ \langle v^2-v \rangle$ is provided. The hulls of cyclic codes over $\Re$ are studied. The average $2$-dimension $E(n)$ of the hulls of cyclic codes over $\Re$ is also…
A cyclic codes of length $n$ over the rings $Z_{2^{m}}$ of integer of modulo $2^{m}$ is a linear code with property that if the codeword $(c_0,c_1,...,c_{n-1})\in \mathcal{C}$ then the cyclic shift $(c_1,c_2,...,c_0)\in \mathcal{C}$.…
Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…
Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes such as cyclic codes, Reed-Solomon codes, and Reed-Muller codes have nice decoding algorithms.…
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…
Burst errors are very common in practice. There have been many designs in order to control and correct such errors. Recently, a new class of byte error control codes called spotty byte error control codes has been specifically designed to…
Pomset block metric is a generalization of pomset metric. In this paper, we define weight enumerator of linear block codes in pomset metric over $\mathbb{Z}_m$ and establish MacWilliams type identities for linear block codes with respect to…
In this paper we define $\mathbb{Z}_{2}\mathbb{Z}_{4}-$Simplex and MacDonald Codes of type $\alpha $ and $\beta $ and we give the covering radius of these codes.
We construct a class of three-Lee-weight and two infinite families of five-Lee-weight codes over the ring $R=\mathbb{F}_2 +v\mathbb{F}_2 +v^2\mathbb{F}_2 +v^3\mathbb{F}_2 +v^4\mathbb{F}_2,$ where $v^5=1.$ The same ring occurs in the quintic…
$(1+pw)$-constacyclic codes of arbitrary length over the non-principal ideal ring $\mathbb{Z}_{p^s} +u\mathbb{Z}_{p^s}$ are studied, where $p$ is a prime, $w\in \mathbb{Z}_{p^s}^{\times}$ and $s$ an integer satisfying $s\geq 2$. First, the…
In this paper, we study skew constacyclic codes over the ring $\mathbb{Z}_{q}R$ where $R=\mathbb{Z}_{q}+u\mathbb{Z}_{q}$, $q=p^{s}$ for a prime $p$ and $u^{2}=0$. We give the definition of these codes as subsets of the ring…
Codes over various metrics such as Rosenbloom-Tsfasman (RT), Lee, etc. have been considered. Recently, codes over poset metrics have been studied. Poset metric is a great generalization of many metrics especially the well-known ones such as…
Recently, some infinite families of binary minimal and optimal linear codes are constructed from simplicial complexes by Hyun {\em et al}. Inspired by their work, we present two new constructions of codes over the ring $\Bbb F_2+u\Bbb F_2$…
We consider additive codes over GF(4) that are self-dual with respect to the Hermitian trace inner product. Such codes have a well-known interpretation as quantum codes and correspond to isotropic systems. It has also been shown that these…
In this paper, we describe a correspondence between a fuzzy linear code and a family of nested linear codes. We also describe the arithmetic of fuzzy linear codes. As a special class of nested linear codes, we consider a family of nested…
In this study, we obtain new classes of linear codes over Hurwitz integers equipped with a new metric. We refer to the metric as Hurwitz metric. The codes with respect to Hurwitz metric use in coded modu- lation schemes based on quadrature…
In \cite{shi2022few-weight}, Shi and Li studied $\mathcal{C}_D$-codes over the ring $\mathcal{R}:=\mathbb{F}_2[x,y]/\langle x^2, y^2, xy-yx\rangle$ and their binary Gray images, where $D$ is derived using certain simplicial complexes. We…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
A code $C$ is called $\Z_p\Z_{p^2}$-linear if it is the Gray image of a $\Z_p\Z_{p^2}$-additive code, where $p>2$ is prime. In this paper, the rank and the dimension of the kernel of $\Z_p\Z_{p^2}$-linear codes are studied. Two bounds of…