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 .