In this article, we study skew cyclic codes over ring R = Fq + vFq + v 2 Fq, where q = p, p is an odd prime and v3 = v. We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomials of the duals of skew cyclic codes. Moreover, the idempotent genera...

In this paper we generalize the notion of cyclicity of codes, that is, θ-polycyclic codes and θ-sequential codes. It is shown that for a code C, C is θ-polycyclic (θ-sequential) if and only if its dual C⊥ is θ−1-sequential (θ−1-polycyclic). Furthermore, we study central θ-constacyclic codes. Mathematics Subject Classification: Primary 94B60; Secondary 94B15, 16W20

Recently, Yaakobi et al. introduced codes for b-symbol read channels, where the read operation is performed as a consecutive sequence of b > 2 symbols. In this paper, we establish a Singleton-type bound on b-symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum bdistance. Based on...

Constacyclic codes may naturally be viewed as objects arising from the cohomological concept of a cocycle. Cohomology theory suggests a transformation which is used to show, under certain circumstances, a cyclic code of length mn over a ring R is isomorphic to the direct sum of m constacyclic codes of length n. In particular this isomorphism holds in many local rings (for example Galois rings) ...

Using geometric properties of the variety Vr,t, the image under the Grassmannian map of a Desarguesian (t− 1)-spread of PG (rt− 1, q), we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We exactly determine the parameters of these codes and characterise the words of minimum weight.

In algebraic coding theory it is common practice to require that (n, q) = 1, where n is the word length and F = GF(q) is the alphabet. In this paper, which is about constacyclic codes, we shall stick to this practice too. Since linear codes have the structure of linear subspaces of F , an alternative description of constacyclic codes in terms of linear algebra appears to be another quite natura...

In this paper a family of constacyclic ternary quasi-perfect linear block codes is presented. This family extends the result presented in a previous work by the first two authors, where the existence of codes with the presented parameters was stated as an open question. The codes have a minimum distance 5 and covering radius 3.