# Spectral Bounds for Quasi-Twisted Codes

## TL;DR

This paper introduces spectral bounds for quasi-twisted codes over finite fields, generalizing existing bounds by leveraging spectral analysis and eigenvalues of polynomial matrices to estimate minimum distances.

## Contribution

It proposes new lower bounds on the minimum distance of quasi-twisted codes using spectral analysis, extending previous bounds like Semenov-Trifonov and Zeh-Ling.

## Key findings

- New spectral bounds improve minimum distance estimates.
- Bounds generalize and extend classical cyclic code bounds.
- Method applies spectral analysis to polynomial matrices.

## Abstract

New lower bounds on the minimum distance of quasi-twisted codes over finite fields are proposed. They are based on spectral analysis and eigenvalues of polynomial matrices. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a manner similar to how the Roos and shift bounds extend the BCH and HT bounds for cyclic codes.