Decoding generalised hyperoctahedral groups and asymptotic analysis of correctible error patterns

TL;DR

This paper introduces a majority-logic decoding algorithm for the generalized hyperoctahedral group as an error-correcting code, analyzes its complexity, and studies the asymptotic behavior of error patterns it can correct.

Contribution

It presents a novel decoding algorithm for the hyperoctahedral group and provides complexity analysis and asymptotic enumeration of correctable error patterns.

Findings

Decoding algorithm successfully corrects certain error patterns.

Complexity of the proposed decoding algorithm is characterized.

Asymptotic analysis of error patterns exceeding correction capability.

Abstract

We demonstrate a majority-logic decoding algorithm for decoding the generalised hyperoctahedral group $C_m \wr S_n$ when thought of as an error-correcting code. We also find the complexity of this decoding algorithm and compare it with that of another, more general, algorithm. Finally, we enumerate the number of error patterns exceeding the correction capability that can be successfully decoded by this algorithm, and analyse this asymptotically.