The MacWilliams Theorem for Four-Dimensional Modulo Metrics

TL;DR

This paper extends the MacWilliams theorem to codes over finite fields equipped with four-dimensional modulo metrics, providing a new theoretical framework for analyzing such codes.

Contribution

It introduces a novel generalization of the MacWilliams theorem applicable to four-dimensional modulo metrics on finite field codes.

Findings

Established the MacWilliams identity for four-dimensional modulo metrics.

Provided theoretical insights into the structure of codes under these metrics.

Potential implications for code design and analysis in higher-dimensional metric spaces.

Abstract

In this paper, the MacWilliams theorem is stated for codes over finite field with four-dimensional modulo metrics.