Lifted MDS Codes over Finite Fields

TL;DR

This paper introduces a method to lift MDS codes from a smaller finite field to a larger one, preserving their distance properties and expanding their applicability in coding theory and related fields.

Contribution

The paper presents a novel technique for lifting MDS codes to higher finite fields while maintaining their optimal distance properties.

Findings

Successfully lifts MDS codes to larger finite fields

Preserves the minimum distance of codes during the lifting process

Enables construction of MDS codes over larger fields from smaller ones

Abstract

MDS codes are elegant constructions in coding theory and have mode important applications in cryptography, network coding, distributed data storage, communication systems et. In this study, a method is given which MDS codes are lifted to a higher finite field. The presented method satisfies the protection of the distance and creating the MDS code over the $F_q$ by using MDS code over $F_p.$