A Novel Lowest Density MDS Array Code

TL;DR

This paper presents a new MDS array code with minimal density, capable of correcting any number of erasures without size restrictions, using a simple matrix-based construction and decoding algorithm.

Contribution

It introduces the first low-density MDS array code that is unrestricted in size and erasure correction, based on totally nonsingular matrices.

Findings

Achieves lowest possible density for MDS array codes.

Supports arbitrary code size and erasure correction.

Features a straightforward decoding algorithm.

Abstract

In this paper we introduce a novel MDS array code with lowest density. In contrast to existing codes, this one has no restrictions on the size or the number of erasures it can correct. It is based on a simple matrix construction involving totally nonsingular matrices. We also introduce a simple decoding algorithm based on the structure of the code.