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Mathematics > Combinatorics

arXiv:2210.07496 (math)
[Submitted on 14 Oct 2022]

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

Authors:Alexander Barg, Alexey Glazyrin, Wei-Jiun Kao, Ching-Yi Lai, Pin-Chieh Tseng, Wei-Hsuan Yu
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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 $n\ge 6$ 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: Main text 23 pp. and Appendix 17pp
Subjects: Combinatorics (math.CO); Information Theory (cs.IT)
Cite as: arXiv:2210.07496 [math.CO]
  (or arXiv:2210.07496v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2210.07496

Submission history

From: Wei-Hsuan Yu [view email]
[v1] Fri, 14 Oct 2022 03:49:15 UTC (34 KB)
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