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

Fuente: arXiv
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Main Authors: Barg, Alexander, Glazyrin, Alexey, Kao, Wei-Jiun, Lai, Ching-Yi, Tseng, Pin-Chieh, Yu, Wei-Hsuan
Format: Preprint
Published: 2022
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author Barg, Alexander
Glazyrin, Alexey
Kao, Wei-Jiun
Lai, Ching-Yi
Tseng, Pin-Chieh
Yu, Wei-Hsuan
author_facet Barg, Alexander
Glazyrin, Alexey
Kao, Wei-Jiun
Lai, Ching-Yi
Tseng, Pin-Chieh
Yu, Wei-Hsuan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2210_07496
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle On the size of maximal binary codes with 2, 3, and 4 distances
Barg, Alexander
Glazyrin, Alexey
Kao, Wei-Jiun
Lai, Ching-Yi
Tseng, Pin-Chieh
Yu, Wei-Hsuan
Combinatorics
Information Theory
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.
title On the size of maximal binary codes with 2, 3, and 4 distances
topic Combinatorics
Information Theory
url https://arxiv.org/abs/2210.07496