weight (strings)WeightStrings2005-04-30 08:39:482005-05-01 15:00:02DefinitionHamming weight% this is the default PlanetMath preamble. as your knowledge
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Let $A$ be an alphabet, $a\in A$ a letter from $A$ and $c\in A^*$ a
string over $a$. Then the $a$-\emph{weight} of $c$, denoted by
$\wt_a(c)$, is the number of times $a$ occurs in $c$.
If $A$ is an abelian group, the \emph{Hamming weight} $\wt(c)$ of $c$ (no \PMlinkescapetext{index}),
often simply referred to as ``weight'', is the number of nonzero letters in $c$.
\subsubsection*{Examples}
\begin{itemize}
\item Let $A=\{x,y,z\}$. In the string $c:=yxxzyyzxyzzyx$, $y$ occurs $5$
times, so the $y$-weight $\wt_y(c)=5$.
\item Let $A=\mbb{Z}_3=\{0,1,2\}$ (an abelian group) and
$c:=002001200$. Then $\wt_0(c)=6$, $\wt_1(c)=1$, $\wt_2(c)=2$ and
$\wt(c)=\wt_1(c)+\wt_2(c)=3$.
\end{itemize}