A transform approach to polycyclic and serial codes over rings
Information Theory
2024-11-11 v1 math.IT
Abstract
In this paper, a transform approach is used for polycyclic and serial codes over finite local rings in the case that the defining polynomials have no multiple roots. This allows us to study them in terms of linear algebra and invariant subspaces as well as understand the duality in terms of the transform domain. We also make a characterization of when two polycyclic ambient spaces are Hamming-isometric.
Cite
@article{arxiv.2105.05046,
title = {A transform approach to polycyclic and serial codes over rings},
author = {Maryam Bajalan and Edgar Martínez-Moro and Steve Szabo},
journal= {arXiv preprint arXiv:2105.05046},
year = {2024}
}