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...

The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this work, we propose a decomposition of the defining set of constacyclic codes. Using this method, we construct four classes of q-ary entanglement-assisted quant...

Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form q = 2am + t, n = q 2 +1 a . Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.

In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes. And we give some results on Hermitian self-dual codes, which are the extended cyclic duadic codes.

For λ an n-th power of a unit in a finite chain ring we prove that λ-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the α+pβconstacyclic codes of length p over the Galois ring GR(p, r).

We present two families of constacyclic linear codes with large automorphism groups. The codes are obtained from the twisted tensor product construction. AMS subject classification: 05E20, 05B25, 11T71, 94B25, 94B27, 51E22, 51E20, 20G40, 14L35

Linear codes may be endowed with cyclic structures by means of skew polynomial rings. This is the case of Piret cyclic convolutional codes [26] and the subsequent generalizations and alternatives (see [27], [14], [11], [25], [16], [20]). Non commutative cyclic structures of this kind have been also considered for block linear codes ([7], [5], [4], [12], [1]), and for linear codes over commutati...