On Multidimensional 2-Weight-Limited Burst-Correcting Codes

TL;DR

This paper explores multidimensional codes designed to correct burst errors of weight at most 2, providing explicit constructions and analyzing their redundancy relative to theoretical lower bounds.

Contribution

It introduces new explicit code constructions for multidimensional burst error correction under various positional constraints and compares their redundancy to lower bounds.

Findings

Explicit code constructions for each error limitation case.

Redundancy of the codes is close to the proven lower bounds.

The study enhances understanding of multidimensional burst error correction capabilities.

Abstract

We consider multidimensional codes capable of correcting a burst error of weight at most $2$. When two positions are in error, the burst limits their relative position. We study three such limitations: the $L_\infty$ distance between the positions is bounded, the $L_1$ distance between the positions is bounded, or the two positions are on an axis-parallel line with bounded distance between them. In all cases we provide explicit code constructions, and compare their excess redundancy to a lower bound we prove.