weight (strings)

Let $A$ be an alphabet, $a\\in A$ a letter from $A$ and $c\\in A^{*}$ astring 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 $\\operatorname{wt}(c)=\\operatorname{wt}_{1}(c)+\\operatorname{wt}_{2}(c)=3$ .

单词	Weightstrings
释义	weight (strings) Let $A$ be an alphabet, $a\\in A$ a letter from $A$ and $c\\in A^{}$ astring 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 $\\operatorname{wt}(c)=\\operatorname{wt}_{1}(c)+\\operatorname{wt}_{2}(c)=3$ .
随便看	UniquenessOfAdditiveIdentityInARing uniqueness of additive identity in a ring UniquenessOfAdditiveInverseInARing uniqueness of additive inverse in a ring UniquenessOfASparseSolution uniqueness of a sparse solution UniquenessOfCardinality uniqueness of cardinality UniquenessOfDigitalRepresentation uniqueness of digital representation UniquenessOfDivisionAlgorithmInEuclideanDomain uniqueness of division algorithm in Euclidean domain UniquenessOfFourierExpansion uniqueness of Fourier expansion Uniqueness of identity proofs and Hedbergâs theorem Uniqueness of inductive types UniquenessOfInverseforGroups uniqueness of inverse (for groups) UniquenessOfLaurentExpansion uniqueness of Laurent expansion UniquenessOfLimitOfSequence uniqueness of limit of sequence UniquenessOfMeasuresExtendedFromApisystem uniqueness of measures extended from a π-system UniquenessOfMoebiusFunction