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arXiv · 2503.15116

Maximum Size $t$-Intersecting Families and Anticodes

Xuan Wang·Tuvi Etzion·Denis Krotov·Minjia Shi
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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\H{o}s-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.

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Xuan Wang, Tuvi Etzion, Denis Krotov, Minjia Shi. 2025-03-19. Maximum Size $t$-Intersecting Families and Anticodes. https://arxiv.org/abs/2503.15116

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