=ADD=
=author=
Brawley Jr.; Joel V. + Lisonek; Petr
=title=
Counting Equivalence Classes of Hadamard Pattern Sets by Group Action Methods
=number=
92-28
=year=
1992
=sponsor=
 Austrian Ministery of Science and Research, Austrian Forschungsf"{o}rderungsfonds,
 project no. P7220. 
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-28.ps.gz
=abstract=
This paper develops mathematical methods for studying
Hadamard pattern sets which are currently used as models
of neural networks. Our main result is an explicit
isomorphism between the stabilizers of Hadamard patterns
and the general linear groups over the finite field
GF(2). This isomorphism carries over the respective
group actions and can be used as a tool for solving
problems related to Hadamard patterns. Two such
applications  are presented in full detail;
specifically, the enumeration of equivalence classes of
Hadamard pattern sets and the evaluation of orbit
lengths. Most of the Work was done with the aid of
CAYLEY, the computer algebra system for group theory

=location=
2
=owner=
2
=source=
3
=reftype=
14