Abstract
Let \( \mathcal{F} \subseteq 2^{[n]}\) be a fixed family of subsets. Let \(D( \mathcal{F} )\) stand for the following set of Hamming distances:
. \( \mathcal{F} \) is said to be a Hamming symmetric family, if \( \mathcal{F} \)X implies \(n-d\in D( \mathcal{F} )\) for each \(d\in D( \mathcal{F} )\).
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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Hegedüs, G. Upper bounds for the size of set systems with a symmetric set of Hamming distances. Acta Math. Hungar. 171, 176–182 (2023). https://doi.org/10.1007/s10474-023-01374-y
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DOI: https://doi.org/10.1007/s10474-023-01374-y