On the size of maximal binary codes with 2, 3, and 4 distances

Authors

Alexander Barg
Alexey Glazyrin, The University of Texas Rio Grande ValleyFollow
Wei-Jiun Kao
Ching-Yi Lai
Pin-Chieh Tseng
Wei-Hsuan Yu

Document Type

Article

Publication Date

6-30-2024

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 n≥6 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.

Comments

Copyright 2024 by the author(s).This work is made available under the terms of a Creative Commons Attribution License, available at https://creativecommons.org/licenses/by/4.0/

Recommended Citation

Barg, Alexander, Alexey Glazyrin, Wei-Jiun Kao, Ching-Yi Lai, Pin-Chieh Tseng, and Wei-Hsuan Yu. 2024. “On the Size of Maximal Binary Codes with 2, 3, and 4 Distances.” Combinatorial Theory 4 (1). https://doi.org/10.5070/C64163844.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Combinatorial Theory

DOI

http://doi.org/10.5070/C64163844