Numbers of isometry classes of block codes
Numbers of isometry classes of block codes
The isometry classes of block codes can also be decribed as orbits under group actions. Given a finite alphabet A of size ≥ 2 then an [n,m]-block code is an m-subset of A
n
. And the group of all isometries can be described as a
wreath product
S
A
≀
S
n
.
Number of isometry classes of [n,m]-block codes over an alphabet of size 2
Number of isometry classes of [n,m]-block codes over an alphabet of size 3
Number of isometry classes of [n,m]-block codes over an alphabet of size 4
harald.fripertinger "at" uni-graz.at, May 10, 2016
Numbers of isometry classes of block codes
