Weight (strings)
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
- Let
. In the string
,
occurs 5 times, so the
-weight of
is
.
- Let
(an abelian group) and
. Then
,
,
and
.
This article incorporates material from Weight (strings) on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.