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...

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.

Let Fq be a finite field of cardinality q, R = Fq[u]/〈u 〉 = Fq+uFq+u 2 Fq+u 3 Fq (u = 0) which is a finite chain ring, and n be a positive integer satisfying gcd(q, n) = 1. For any δ, α ∈ F×q , an explicit representation for all distinct (δ + αu)-constacyclic codes over R of length n is given, and the dual code for each of these codes is determined. For the case of q = 2 and δ = 1, all self-dua...

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...

Let F2m be a finite field of cardinality 2 , R = F2m [u]/〈u 〉) and n is an odd positive integer. For any δ, α ∈ F2m , ideals of the ring R[x]/〈x 2n − (δ+αu)〉 are identified as (δ + αu)-constacyclic codes of length 2n over R. In this paper, an explicit representation and enumeration for all distinct (δ + αu)constacyclic codes of length 2n over R are presented.