Roos bound for skew cyclic codes in Hamming and rank metric

https://doi.org/10.1016/j.ffa.2020.101772Get rights and content
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Abstract

In this paper, a Roos like bound on the minimum distance for skew cyclic codes over a general field is provided. The result holds in the Hamming metric and in the rank metric. The proofs involve arithmetic properties of skew polynomials and an analysis of the rank of parity-check matrices. For the rank metric case, a way to arithmetically construct codes with a prescribed minimum rank distance, using the skew Roos bound, is also given. Moreover, some examples of MDS codes and MRD codes over finite fields are built, using the skew Roos bound.

MSC

11T71
94B65
16S36

Keywords

Cyclic codes
Skew cyclic codes
Roos bound
Rank-metric codes
MRD codes

Cited by (0)

Research partially supported by grant PID2019-110525GB-I00 from Agencia Estatal de Investigación (AEI) and from Fondo Europeo de Desarrollo Regional (FEDER), and from Swiss National Science Foundation through grants no. 187711 and 188430.