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capitalized Hamming (else it looks pork-related); like +-> as
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David Handelman
David Handelman
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Union of hammingHamming balls

Let $V \subseteq \{0,1\}^n$, $\log|V| = k$. Consider

$V_r:= \bigcup_{x \in V} V_r(x)$, where $V_r(x)$ is a Hamming full-ball of radius $r$ and the center $x$.

What is a lower bound for the cardinality of $V_r$? DoesIs the cardinality of $V_r$ is the smallest when $V$ is a Hamming full-ball (likeas in Harper's theorem)?

Union of hamming balls

Let $V \subseteq \{0,1\}^n$, $\log|V| = k$. Consider

$V_r:= \bigcup_{x \in V} V_r(x)$, where $V_r(x)$ is a Hamming full-ball of radius $r$ and the center $x$.

What is a lower bound for the cardinality of $V_r$? Does the cardinality of $V_r$ is the smallest when $V$ is a Hamming full-ball (like in Harper's theorem)?

Union of Hamming balls

Let $V \subseteq \{0,1\}^n$, $\log|V| = k$. Consider

$V_r:= \bigcup_{x \in V} V_r(x)$, where $V_r(x)$ is a Hamming full-ball of radius $r$ and center $x$.

What is a lower bound for the cardinality of $V_r$? Is the cardinality of $V_r$ the smallest when $V$ is a Hamming full-ball (as in Harper's theorem)?

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Alexey Milovanov
Alexey Milovanov
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Union of hamming balls

Let $V \subseteq \{0,1\}^n$, $\log|V| = k$. Consider

$V_r:= \bigcup_{x \in V} V_r(x)$, where $V_r(x)$ is a Hamming full-ball of radius $r$ and the center $x$.

What is a lower bound for the cardinality of $V_r$? Does the cardinality of $V_r$ is the smallest when $V$ is a Hamming full-ball (like in Harper's theorem)?