New MDS Euclidean Self-orthogonal Codes

TL;DR

This paper introduces a new criterion for MDS Euclidean self-orthogonal codes and constructs numerous new codes, significantly expanding the known classes of such codes over finite fields, especially for large square q.

Contribution

The paper presents a novel criterion for MDS Euclidean self-orthogonal codes and constructs a large number of new codes with various lengths and dimensions, advancing coding theory.

Findings

Constructed about  q new MDS Euclidean (almost) self-dual codes for large square q.

Produced about  q new MDS Euclidean self-orthogonal codes with different even lengths.

Established a criterion for identifying MDS Euclidean self-orthogonal codes.

Abstract

In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$, about $\frac{1}{8}\cdot q$ new MDS Euclidean (almost) self-dual codes over $\F_q$ can be produced. Moreover, we can construct about $\frac{1}{4}\cdot q$ new MDS Euclidean self-orthogonal codes with different even lengths $n$ with dimension $\frac{n}{2}-1$.