Abelian and consta-Abelian polyadic codes over affine algebras with a finite commutative chain coefficient ring

TL;DR

This paper introduces Abelian and consta-Abelian polyadic codes over affine algebra rings with chain coefficients, analyzing their structure and enumeration using classical group splitting methods.

Contribution

It extends the theory of polyadic codes to affine algebra rings over chain rings, providing new structural insights and enumeration results.

Findings

Derived structural properties of polyadic codes over affine algebras

Established enumeration formulas for these codes

Connected classical group splittings to code construction

Abstract

In this paper, we define Abelian and consta-Abelian polyadic codes over rings defined as affine algebras over chain rings. For that aim, we use the classical construction via splittings and multipliers of the underlying Abelian group. We also derive some results on the structure of the associated polyadic codes and the number of codes under these conditions.