Explicit MDS Codes with Complementary Duals

TL;DR

This paper presents explicit constructions of LCD MDS codes using algebraic function fields, expanding the known classes of optimal codes with applications in communication and security.

Contribution

It introduces new explicit constructions of LCD MDS codes over odd characteristic fields using algebraic function fields.

Findings

Constructed several classes of explicit LCD MDS codes

Codes are applicable in communication and security systems

Provides algebraic methods for code construction

Abstract

In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on. LCD codes have been extensively studied in literature. On the other hand, MDS codes form an optimal family of classical codes which have wide applications in both theory and practice. The main purpose of this paper is to give an explicit construction of several classes of LCD MDS codes, using tools from algebraic function fields. We exemplify this construction and obtain several classes of explicit LCD MDS codes for the odd characteristic case.