# Questions tagged [hamming-distance]

The hamming-distance tag has no usage guidance.

6
questions

**2**

votes

**0**answers

247 views

### Primes with given Hamming weight

If I understand correctly, in the following MO-thread
Are There Primes of Every Hamming Weight?
two users of the site claim that it has been already proven that, for every sufficiently large $n \in \...

**4**

votes

**1**answer

206 views

### Conjecture about infinite word

Let $w=a_1a_2a_3...$ be an infinite word over a finite alphabet and $\epsilon>0$. Do there exist integers $n,k$ such that $\frac{d(a_1a_2...a_n,a_{k+1}a_{k+2}...a_{k+n})}{n}<\epsilon$ ?
($d(u,v)$...

**4**

votes

**1**answer

110 views

### 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 ...

**0**

votes

**1**answer

118 views

### 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**

votes

**1**answer

328 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 $...

**2**

votes

**1**answer

66 views

### 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\...