An Unified Approach on Constructing of MDS Self-dual Codes via Reed-Solomon Codes

TL;DR

This paper introduces a unified method for constructing MDS self-dual codes over finite fields, simplifying existing results and providing new constructions, thereby advancing coding theory.

Contribution

It offers a unified framework that simplifies previous constructions and introduces new methods for creating MDS self-dual codes.

Findings

Unified approach reproduces previous results with concise proofs

New constructions of MDS self-dual codes are provided

Raises open problems for future research

Abstract

Based on the fundamental results on MDS self-dual codes over finite fields constructed via generalized Reed-Solomon codes \cite{JX} and extended generalized Reed-Solomon codes \cite{Yan}, many series of MDS self-dual codes with different length have been obtained recently by a variety of constructions and individual computations. In this paper, we present an unified approach to get several previous results with concise statements and simplified proofs, and some new constructions on MDS self-dual codes. In the conclusion section we raise two open problems.