Twisted Reed-Solomon Codes

TL;DR

This paper introduces a new construction method for MDS codes over finite fields, producing numerous new codes with lengths at least half the field size, many of which are not equivalent to Reed-Solomon codes.

Contribution

It provides a novel general construction of MDS codes and explicitly identifies subclasses with new codes that extend beyond traditional Reed-Solomon codes.

Findings

New MDS codes of length at least q/2 for all q ≥ 11

Most new codes are not equivalent to Reed-Solomon codes

Explicit subclasses demonstrating the construction

Abstract

We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the new codes are not equivalent to a Reed-Solomon code.