On polycyclic linear and additive codes associated to a trinomial over a finite chain ring
Information Theory
2025-03-18 v1 math.IT
Abstract
In this paper, we investigate polycyclic codes associated with a trinomial of arbitrary degree over a finite chain ring We extend the concepts of -isometry and -equivalence known for constacyclic codes to this class of codes, providing a broader framework for their structural analysis. We describe the classes of -equivalence and compute their number, significantly reducing the study of trinomial codes over . Additionally, we examine the special case of trinomials of the form and analyze their implications. Finally, we consider the extension of our results to certain trinomial additive codes over
Keywords
Cite
@article{arxiv.2503.11765,
title = {On polycyclic linear and additive codes associated to a trinomial over a finite chain ring},
author = {Abdelghaffar Chibloun and Hassan Ou-azzou and Edgar Martínez-Moro and Mustapha Najmeddine},
journal= {arXiv preprint arXiv:2503.11765},
year = {2025}
}