Maximum Size $t$-Intersecting Families and Anticodes Full article
| Journal |
Electronic Journal of Combinatorics
ISSN: 1077-8926 , E-ISSN: 1097-1440 |
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| Output data | Year: 2026, Volume: 33, Number: 1, DOI: 10.37236/14074 | ||||||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
The maximum size of t-intersecting families is one of the most celebrated topics in combinatorics, and its size is known as the Erd}os-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 maxi mum 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.
Cite:
Wang X.
, Etzion T.
, Krotov D.S.
, Shi M.
Maximum Size $t$-Intersecting Families and Anticodes
Electronic Journal of Combinatorics. 2026. V.33. N1. DOI: 10.37236/14074 WOS OpenAlex
Maximum Size $t$-Intersecting Families and Anticodes
Electronic Journal of Combinatorics. 2026. V.33. N1. DOI: 10.37236/14074 WOS OpenAlex
Dates:
| Submitted: | Apr 14, 2025 |
| Accepted: | Nov 2, 2025 |
| Published online: | Jan 23, 2026 |
Identifiers:
| Web of science: | WOS:001673882000001 |
| OpenAlex: | W7125429467 |
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