Construction of MDS self-dual codes from generalized Reed-Solomon codes

TL;DR

This paper constructs new classes of MDS self-dual codes over finite fields with odd characteristic using (extended) generalized Reed-Solomon codes, advancing the understanding of such codes' existence.

Contribution

It introduces novel constructions of MDS self-dual codes over finite fields of odd characteristic via (extended) generalized Reed-Solomon codes.

Findings

New classes of MDS self-dual codes constructed

Extended generalized Reed-Solomon codes used in construction

Advances understanding of MDS self-dual codes over odd fields

Abstract

MDS codes and self-dual codes are important families of classical codes in coding theory. It is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field $F_q$ is completely solved for $q$ is even. In this paper, for finite field with odd characteristic, we construct some new classes of MDS self-dual codes by (extended) generalized Reed-Solomon codes.