具有汉明距离对称集的集系统大小的上界

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2023-11-03 DOI:10.1007/s10474-023-01374-y

G. Hegedüs

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引用次数: 0

摘要

设$ \mathcal{F} \subseteq 2^{[n]}$为一个固定的子集族。让$D( \mathcal{F} )$代表以下一组汉明距离:$$D( \mathcal{F} ):=\{d_H(F,G) : F, G\in \mathcal{F} ,\ F\neq G\}$$。假设$ \mathcal{F} $是一个汉明对称族，如果$ \mathcal{F} $ X对每个$d\in D( \mathcal{F} )$表示$n-d\in D( \mathcal{F} )$，我们给出汉明对称族大小的明确上界。我们的证明是基于线性代数的界法。

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

Let $ \mathcal{F} \subseteq 2^{[n]}$ be a fixed family of subsets. Let $D( \mathcal{F} )$ stand for the following set of Hamming distances:

$$D( \mathcal{F} ):=\{d_H(F,G) : F, G\in \mathcal{F} ,\ F\neq G\}$$

. $ \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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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.