Upper bounds for the size of set systems with a symmetric set of Hamming distances

2023/04/30 by Hegedüs, Gábor
#05D05 #12D99 #15A03 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.00433

Abstract

Let \cal F⊆ 2^[n] be a fixed family of subsets. Let D(\cal F) stand for the following set of Hamming distances: D(\cal F):=\d_H(F,G):~ F, G∈ \cal F, F≠ G\. \cal F is said to be a Hamming symmetric family, if d∈ D(\cal F) implies n-d∈ D(\cal F) for each d∈ D(\cal F). We give sharp upper bounds for the size of Hamming symmetric families. Our proof is based on the linear algebra bound method.

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