New MDS Self-Dual Codes over Large Finite Fields

TL;DR

This paper presents the construction of maximum distance separable (MDS) self-dual codes over large finite fields, utilizing cyclic and negacyclic duadic codes for both Euclidean and Hermitian cases.

Contribution

It introduces new MDS self-dual codes over large finite fields derived from cyclic and negacyclic duadic codes, expanding the known classes of such codes.

Findings

Constructed MDS Euclidean self-dual codes over large fields.

Developed Hermitian self-dual codes using duadic code structures.

Demonstrated the applicability of cyclic and negacyclic codes in self-dual code construction.

Abstract

We construct MDS Euclidean and Hermitian self-dual codes over large finite fields of odd and even characteristics. Our codes arise from cyclic and negacyclic duadic codes.