On depth spectra of constacyclic codes

TL;DR

This paper characterizes the depth spectra of all repeated-root constacyclic codes over finite chain rings, providing a comprehensive understanding of their structure with illustrative examples.

Contribution

It determines the depth spectra of all repeated-root constacyclic codes over finite chain rings, extending previous results to arbitrary lengths.

Findings

Explicit formulas for depth spectra of these codes

Classification of codes based on their depth spectra

Examples illustrating the theoretical results

Abstract

In this paper, we determine depth spectra of all repeated-root $(\alpha+\gamma \beta)$-constacyclic codes of arbitrary lengths over a finite commutative chain ring $\mathcal{R},$ where $\alpha$ is a non-zero element of the Teichm\"{u}ller set of $\mathcal{R},$ $\gamma$ is a generator of unique maximal ideal of $\mathcal{R}$ and $\beta$ is a unit in $\mathcal{R}.$ We also illustrate our results with some examples.