On the size of maximal binary codes with 2, 3, and 4 distances
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912474831257600 |
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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 |
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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 |