Maximum Size $t$-Intersecting Families and Anticodes
Combinatorics
2025-03-20 v1
Abstract
The maximum size of -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 -intersecting families and their associated maximum size constant-weight anticodes over alphabet of size . 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.
Keywords
Cite
@article{arxiv.2503.15116,
title = {Maximum Size $t$-Intersecting Families and Anticodes},
author = {Xuan Wang and Tuvi Etzion and Denis Krotov and Minjia Shi},
journal= {arXiv preprint arXiv:2503.15116},
year = {2025}
}