Construction of MDS self-dual codes from orthogonal matrices

TL;DR

This paper presents algorithms for constructing self-dual codes over finite fields using orthogonal matrices, achieving optimal and near-optimal codes with various properties.

Contribution

It introduces new methods utilizing orthogonal matrices and randomization to construct self-dual codes, including optimal and MDS codes.

Findings

Constructed optimal self-dual codes over small and large prime fields.

Developed algorithms using orthogonal matrices and code extension.

Achieved near MDS and MDS self-dual codes.

Abstract

In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.