A transform approach to polycyclic and serial codes over rings

TL;DR

This paper introduces a transform-based method for analyzing polycyclic and serial codes over finite local rings, enabling linear algebraic study, duality understanding, and isometry characterization.

Contribution

It presents a novel transform approach for polycyclic and serial codes over rings, facilitating their analysis and classification in the transform domain.

Findings

Transform approach simplifies code analysis over rings

Duality is characterized via the transform domain

Conditions for Hamming-isometry of polycyclic spaces are provided

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.