A heuristic approach for designing cyclic group codes

TL;DR

This paper introduces a heuristic method for designing cyclic group codes by distributing points on a sphere, achieving comparable performance to brute-force methods but with lower complexity, enabling higher-dimensional code design.

Contribution

A novel heuristic technique for constructing cyclic group codes that is efficient and scalable to higher dimensions compared to traditional brute-force approaches.

Findings

Heuristic approach performs comparably to brute-force search.

Method enables designing codes with many points in high dimensions.

Numerical experiments confirm effectiveness across various dimensions.

Abstract

In this paper we propose a heuristic technique for distributing points on the surface of a unit n-dimensional Euclidean sphere, generated as the orbit of a finite cyclic subgroup of orthogonal matrices, the so called cyclic group codes. Massive numerical experiments were done and many new cyclic group codes have been obtained in several dimensions at various rate. The obtained results assure that the heuristic approach have performance comparable to a brute-force search technique with the advantage of having low complexity, allowing for designing codes with a large number of points in higher dimensions.