Explicit Constructions of Quasi-Uniform Codes from Groups

TL;DR

This paper presents explicit methods for constructing quasi-uniform codes from groups, detailing code parameters and exploring applications in affine and network coding.

Contribution

It provides explicit constructions of quasi-uniform codes from both abelian and nonabelian groups, including parameter determination.

Findings

Codebook size and minimum distance are derived from group properties.

Applicable to almost affine and non-linear network codes.

Explicit constructions enable practical code design.

Abstract

We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian groups. Potentials applications comprise the design of almost affine codes and non-linear network codes.