Weight (strings) explained
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
.
Examples
. In the string
,
occurs 5 times, so the
-weight of
is
.
(an abelian group) and
. Then
,
,
and
.
