On the size of maximal binary codes with 2, 3, and 4 distances
Combinatorics
2025-07-14 v1 Information Theory
math.IT
Abstract
We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths as well as the exact size of maximal binary constant weight codes with 2,3, and 4 distances for several values of the weight and for all but small lengths.
Cite
@article{arxiv.2210.07496,
title = {On the size of maximal binary codes with 2, 3, and 4 distances},
author = {Alexander Barg and Alexey Glazyrin and Wei-Jiun Kao and Ching-Yi Lai and Pin-Chieh Tseng and Wei-Hsuan Yu},
journal= {arXiv preprint arXiv:2210.07496},
year = {2025}
}
Comments
Main text 23 pp. and Appendix 17pp