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The -weight of a string, for a letter , is the number of times that letter occurs in the string. More precisely, let be a finite set (called the alphabet), a letter of , and a
string (where is the free monoid generated by the elements of , equivalently the set of strings, including the empty string, whose letters are from ). Then the -weight of , denoted by , is the number of times the generator occurs in the unique expression for as a product (concatenation) of letters in .
If is an abelian group, the Hamming weight of ,
often simply referred to as "weight", is the number of nonzero letters in .
- Let . In the string , occurs 5 times, so the -weight of is .
- Let (an abelian group) and . Then , , and .
This article incorporates material from Weight (strings) on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.