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.
Roos bound for skew cyclic codes in Hamming and rank metric / Alfarano, G. N.; Lobillo, F. J.; Neri, A.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 69:(2021). [10.1016/j.ffa.2020.101772]
Roos bound for skew cyclic codes in Hamming and rank metric
Neri A.
2021
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
