Constructions of MDS Self-dual Codes from Short length

TL;DR

This paper presents new methods for constructing maximum distance separable (MDS) self-dual codes of short length using generalized Reed-Solomon codes, expanding the known classes of such codes.

Contribution

It provides explicit constructions of MDS Euclidean self-dual codes for short lengths and introduces new classes of these codes via GRS and extended GRS codes.

Findings

Exact constructions for lengths 3, 4, 5, 6.

New classes of q-ary MDS Euclidean self-dual codes.

Enhanced methods for code construction from known codes.

Abstract

Systematic constructions of MDS self-dual codes is widely concerned. In this paper, we consider the constructions of MDS Euclidean self-dual codes from short length. Indeed, the exact constructions of MDS Euclidean self-dual codes from short length ($n=3,4,5,6$) are given. In general, we construct more new of $q$-ary MDS Euclidean self-dual codes from MDS self-dual codes of known length via generalized Reed-Solomon (GRS for short) codes and extended GRS codes.