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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.15116 |
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| _version_ | 1866908275130236928 |
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| author | Wang, Xuan Etzion, Tuvi Krotov, Denis Shi, Minjia |
| author_facet | Wang, Xuan Etzion, Tuvi Krotov, Denis Shi, Minjia |
| contents | The maximum size of $t$-intersecting families is one of the most celebrated topics in combinatorics, and its size is known as the Erdős-Ko-Rado theorem. Such intersecting families, also known as constant-weight anticodes in coding theory, were considered in a generalization of the well-known sphere-packing bound. In this work we consider the maximum size of $t$-intersecting families and their associated maximum size constant-weight anticodes over alphabet of size $q >2$. It is proved that the structure of the maximum size constant-weight anticodes with the same length, weight, and diameter, depends on the alphabet size. This structure implies some hierarchy of constant-weight anticodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15116 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum Size $t$-Intersecting Families and Anticodes Wang, Xuan Etzion, Tuvi Krotov, Denis Shi, Minjia Combinatorics The maximum size of $t$-intersecting families is one of the most celebrated topics in combinatorics, and its size is known as the Erdős-Ko-Rado theorem. Such intersecting families, also known as constant-weight anticodes in coding theory, were considered in a generalization of the well-known sphere-packing bound. In this work we consider the maximum size of $t$-intersecting families and their associated maximum size constant-weight anticodes over alphabet of size $q >2$. It is proved that the structure of the maximum size constant-weight anticodes with the same length, weight, and diameter, depends on the alphabet size. This structure implies some hierarchy of constant-weight anticodes. |
| title | Maximum Size $t$-Intersecting Families and Anticodes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.15116 |