Multivariable codes in principal ideal polynomial quotient rings with applications to additive modular bivariate codes over $\mathbb{F}_4$

TL;DR

This paper investigates the structure of multivariable modular codes over finite chain rings within principal ideal rings and explores their applications to additive modular codes over , enhancing understanding of code algebraic properties.

Contribution

It characterizes multivariable modular codes over principal ideal rings and applies these findings to additive modular codes over , offering new insights into their algebraic structure.

Findings

Structural description of multivariable modular codes

Application to additive modular codes over 

Enhanced understanding of code algebraic properties

Abstract

In this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field $\mathbb{F}_4$.