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Questions tagged [hamming-distance]

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4
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Hamming representability of finite graphs

This is a follow up on an older question. We construct graph on the vertex set $\{0,1\}^n$ where $n$ is a positive integer. For $x,y \in \{0,1\}^n$ the Hamming distance of $x,y$ is the cardinality of ...
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Conjecture on representing graphs within $\{0,1\}^n$

We construct graph on the vertex set $\{0,1\}^n$ where $n$ is a positive integer. For $x,y \in \{0,1\}^n$ the Hamming distance of $x,y$ is the cardinality of the set $\{ i \in \{0, ..., n-1\} : x(i) \...
4
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1answer
297 views

Spreading $n$ points in $\{0,1\}^n$ as far as possible

Given a positive integer $n$, the Hamming distance $d^H_n(x,y)$ of $x,y\in \{0,1\}^n$ is defined by $$d^H_n(x,y) = |\{k\in\{0,\ldots,n-1\}: x(k)\neq y(k)\}|.$$ We say that a positive integer $s$ is $...
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1answer
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Stretching map of $n$ points from $\{0,1\}^n$ to $\{0,1\}^{n+1}$ with respect to their Hamming distance

Given a positive integer $n$, the Hamming distance $d^H_n(x,y)$ of $x,y\in \{0,1\}^n$ is defined by $$d^H_n(x,y) = |\{k\in\{0,\ldots,n-1\}: x(k)\neq y(k)\}|.$$ Given an integer $n>0$ and a set $S\...