Nearly MDS expander codes with reduced alphabet size

TL;DR

This paper introduces a modification to existing nearly MDS expander code constructions, reducing the required alphabet size by using mixed-alphabet MDS codes, with minimal impact on code rate.

Contribution

It presents a simple modification to prior methods, achieving smaller alphabet sizes for nearly MDS expander codes while maintaining high performance.

Findings

Reduced alphabet size for nearly MDS codes

Minimal decrease in code rate

Effective use of mixed-alphabet MDS codes

Abstract

Recently, Roth and Skachek proposed two methods for constructing nearly maximum-distance separable (MDS) expander codes. We show that through the simple modification of using mixed-alphabet codes derived from MDS codes as constituent codes in their code designs, one can obtain nearly MDS codes of significantly smaller alphabet size, albeit at the expense of a (very slight) reduction in code rate.