weight (strings)

Let $A$ be an alphabet, $a\in A$ a letter from $A$ and $c\in A^{*}$ a string over $a$ . Then the $a$ -weight of $c$ , denoted by $\operatorname{wt}_{a}(c)$ , is the number of times $a$ occurs in $c$ .

If $A$ is an abelian group, the Hamming weight $\operatorname{wt}(c)$ of $c$ (no ), often simply referred to as “weight”, is the number of nonzero letters in $c$ .

Examples

•

Let $A=\{x,y,z\}$ . In the string $c:=yxxzyyzxyzzyx$ , $y$ occurs $5$ times, so the $y$ -weight $\operatorname{wt}_{y}(c)=5$ .
•

Let $A=\mathbb{Z}_{3}=\{0,1,2\}$ (an abelian group) and $c:=002001200$ . Then $\operatorname{wt}_{0}(c)=6$ , $\operatorname{wt}_{1}(c)=1$ , $\operatorname{wt}_{2}(c)=2$ and $\operatorname{wt}(c)=\operatorname{wt}_{1}(c)+\operatorname{wt}_{2}(c)=3$ .

Title	weight (strings)
Canonical name	Weightstrings
Date of creation	2013-03-22 15:13:17
Last modified on	2013-03-22 15:13:17
Owner	GrafZahl (9234)
Last modified by	GrafZahl (9234)
Numerical id	6
Author	GrafZahl (9234)
Entry type	Definition
Classification	msc 94A55
Synonym	weight
Related topic	KleeneStar
Defines	Hamming weight