New constructions of MDS codes with complementary duals

TL;DR

This paper introduces new methods for constructing LCD MDS codes using generalized Reed-Solomon codes, expanding on previous results and enhancing their applicability in communication and cryptography.

Contribution

It proposes a novel approach to construct LCD MDS codes from generalized Reed-Solomon codes, extending existing results and providing new code constructions.

Findings

New LCD MDS codes constructed from generalized Reed-Solomon codes

Extended previously known results on LCD MDS codes

Enhanced code parameters for cryptography and communication

Abstract

Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This application of LCD codes renewed the interest in the construction of LCD codes having a large minimum distance. MDS codes are optimal in the sense that the minimum distance cannot be improved for given length and code size. Constructing LCD MDS codes is thus of significance in theory and practice. Recently, Jin (\cite{Jin}, IEEE Trans. Inf. Theory, 2016) constructed several classes of LCD MDS codes through generalized Reed-Solomon codes. In this paper, a different approach is proposed to obtain new LCD MDS codes from generalized Reed-Solomon codes. Consequently, new code constructions are provided and certain previously known results in \cite{Jin} are extended.