The a -weight of a string, for a a letter, is the number of times that letter occurs in the string. More precisely, let A be a finite set (called the alphabet), a ∈ A a letter of A , and c ∈ A ∗ a string (where A ∗ is the free monoid generated by the elements of A , equivalently the set of strings, including the empty string, whose letters are from A ). Then the a -weight of c , denoted by w t a ( c ) , is the number of times the generator a occurs in the unique expression for c as a product (concatenation) of letters in A .
If A is an abelian group, the Hamming weight w t ( c ) of c , often simply referred to as "weight", is the number of nonzero letters in c .
