Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z 4 + uZ 4 of any length are studied. A new Gray map between Z 4 + uZ 4 and Z 4 (4) is defined. By means of this map, it is shown that the Z 4 Gray image of a (1 + u)-constacyclic code of length n over ...

io-port 06440419 Chen, Jianzhang; Li, Jianping; Huang, Yuanyuan; Lin, Jie Some families of asymmetric quantum codes and quantum convolutional codes from constacyclic codes. Linear Algebra Appl. 475, 186-199 (2015). Summary: Quantum maximal-distance-separable (MDS) codes are an important class of quantum codes. Recently, many scholars utilize constacyclic codes to construct some quantum MDS code...

In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R = Z3+vZ3+v 2 Z3, v 3 = v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasicyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains its dual has been given. The paramete...

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In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal parameters. In this light, we propose constructions of families of classical block and convolutional maximum-distance-separable (MDS) constacyclic codes, as we...

In this paper, we study skew cyclic and skew constacyclic codes over the ring R = Fq + uFq + vFq + uvFq where q = p^m; p is an odd prime, u^2 = u; v^2 = v; uv = vu. We show that Gray image of a skew cyclic code of length n is a skew quasi-cyclic code of length 4n over Fq of index 4. We also study the structural properties of skew cyclic and skew constacyclic codes over R. Further, generating po...

In this paper, we study Z2Z2[u]-(1 + u)-additive constacyclic code of arbitrary length. Firstly, we study the algebraic structure of this family of codes and a set of generator polynomials for this family as a (Z2+uZ2)[x]-submodule of the ring Rα,β. Secondly, we give the minimal generating sets of this family codes, and we determine the relationship of generators between the Z2Z2[u]-(1 + u)-add...

Let $R=\mathbb{Z}_4+u\mathbb{Z}_4,$ where $\mathbb{Z}_4$ denotes the ring of integers modulo $4$ and $u^2=0$. In the present paper, we introduce a new Gray map from $R^n$ to $\mathbb{Z}_{4}^{2n}.$ We study $(1+2u)$-constacyclic codes over $R$ of odd lengths with the help of cyclic codes over $R$. It is proved that the Gray image of $(1+2u)$-constacyclic codes of length $n$ over $R$ are cyclic c...

In this paper we investigate the structure of repeated root constacyclic codes of length 2mp over Fps with a ≥ 1 and (m, p) = 1. We characterize the codes in terms of their generator polynomials. This provides simple conditions on the existence of self-dual negacyclic codes. Further, we gave cases where the constacyclic codes are equivalent to cyclic codes.