A heuristic approach for designing cyclic group codes

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 conducted and many new cyclic group codes have been obtained in several dimensions at various rates. The results assure that the performance of the heuristic approach is comparable to a brute‐force search technique with the advantage of having low complexity, which allows designing codes with a large number of points in high dimensions.