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
.
