Let

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 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.

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cosets in the defining set of constacyclic codes, we constructed three classes of new EAQECCs which satisfy the entanglement-assisted quantum Singleton bound. Besides, three classes of EAQECCs with maximal entanglement fr...

(1+pw)-constacyclic codes of arbitrary length over the nonprincipal ideal ring Zps + uZps are studied, where p is a prime, w ∈ Z × ps and s an integer satisfying s ≥ 2. First, the structure of any (1 + pw)constacyclic code over Zps +uZps are presented. Then enumerations for the number of all codes and the number of codewords in each code, and the structure of dual codes for these codes are give...

The results of J. F. Qian et al. [5] on (1 − γ)-constacyclic codes over finite chain rings of nilpotency index 2 are extended to (1 − γe)constacyclic codes over finite chain rings of arbitrary nilpotency index e+1. The Gray map is introduced for this type of rings. We prove that the Gray image of a linear (1− γe)-constacyclic code over a finite chain ring is a distance-invariant quasi-cyclic co...