Decoding of Matrix-Product Codes

TL;DR

This paper introduces a decoding algorithm for matrix-product codes, capable of correcting errors up to half the minimum distance, with extensions allowing decoding beyond traditional limits in certain cases.

Contribution

It presents a novel decoding algorithm for matrix-product codes and extends it to improve error correction capabilities in specific scenarios.

Findings

Decodes up to half the minimum distance of the code.

Extensions enable decoding beyond standard error correction limits.

Applicable to a class of matrix-product codes.

Abstract

We propose a decoding algorithm for the $(u\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one can decode beyond the error correction capability of the code.