Symbol-pair code is a new coding framework which is proposed to correct errors in the symbolpair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pairdistance five or six. ...

A Correction to this paper has been published: https://doi.org/10.1007/s12095-022-00602-6

In this paper, we give an important isomorphism between contacyclic codes and cyclic codes,over finite principal ideal rings.Necessary and sufficient conditions for the existence of non-trivial cyclic self-dual codes over finite principal ideal rings are given.

We present a new approach to the theory of cyclic and constacyclic codes and generalize the theory to cover the family of additive (not necessarily linear) cyclic codes. The approach is based on the action of the Galois group (cyclotomic cosets). The conventional representation of cyclic codes as ideals in a factor ring of the polynomial ring is not needed. 1 General facts on linear codes The c...

Abstract. Previously, self-dual codes have been constructed from weighing matrices, and in particular from conference matrices (skew and symmetric). In this paper, codes constructed from matrices of skew symmetric type whose determinants reach the EhlichWojtas’ bound are presented. A necessary and sufficient condition for these codes to be self-dual is given, and examples are provided for lengt...