Generalized Spectral Bound for Quasi-Twisted Codes

TL;DR

This paper extends spectral bounds to quasi-twisted codes, demonstrating that the new bounds are tighter and outperform existing bounds like Jensen and Ezerman et al. in many cases.

Contribution

It generalizes the spectral bound approach to quasi-twisted codes, providing improved minimum distance lower bounds.

Findings

New spectral bounds outperform Jensen bound in many cases

Tighter lower bounds on minimum distance for quasi-twisted codes

Extension of spectral theory to a broader class of codes

Abstract

Semenov and Trifonov [22] developed a spectral theory for quasi-cyclic codes and formulated a BCH-like minimum distance bound. Their approach was generalized by Zeh and Ling [24], by using the HT bound. The first spectral bound for quasi-twisted codes appeared in [7], which generalizes Semenov-Trifonov and Zeh-Ling bounds, but its overall performance was observed to be worse than the Jensen bound. More recently, an improved spectral bound for quasi-cyclic codes was proposed in [15], which outperforms the Jensen bound in many cases. In this paper, we adopt this approach to quasi-twisted case and we show that this new generalized spectral bound provides tighter lower bounds on the minimum distance compared to the Jensen and Ezerman et. al. bounds.