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
is the free monoid
generated by the elements of
, equivalently the set of strings, including the empty string, whose letters are from
). Then the
, 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 .