English

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 nn over a finite chain ring R. R. We extend the concepts of n n -isometry and n n -equivalence known for constacyclic codes to this class of codes, providing a broader framework for their structural analysis. We describe the classes of nn-equivalence and compute their number, significantly reducing the study of trinomial codes over RR. Additionally, we examine the special case of trinomials of the form xna1xa0R[x] x^n - a_1x - a_0 \in R[x] and analyze their implications. Finally, we consider the extension of our results to certain trinomial additive codes over R. R.

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}
}
R2 v1 2026-06-28T22:21:09.919Z