Paper Info
Title
The Discovery of Simple 7-Designs with Automorphism Group PTL (2, 32)
Abstract
A computer package is being developed at Bayreuth for the generation and investigation of discrete structures. The package is a C and C++ class library of powerful algorithms endowed with some graph- ical interface modules. Some standard applications can be run automat- ically whereas research projects mostly require small C or C++ pro- grams. The basic philosophy behind the system is to transform problems into standard problems of e.g. group theory, graph theory, linear alge- bra, graphics, or databases and use highly specialized routines from that eld to tackle the problems. The transformations required often follow the same principles especially in questions about generation and isomor- phism testing. We therefore explain some of this background. We relate orbit problems to double cosets and oer a way to solve double coset problems in many important cases. Since the graph isomorphism problem is equivalent to some double coset problem, no polynomial algo- rithm can be expected in general. But the reduction techniques used still allow to solve problems of an interesting size. As examples we explain how the 7-designs in the title were found and how representatives for all isomorphism types of codes or graphs of a certain size can be obtained. The two simple 7-designs with parameters 7-(33,8,10) and 7-(33,8,16) are presented in this paper for the
Year
DOI
Venue
1995
10.1007/3-540-60114-7_10
AAECC
Keywords
Field
DocType
simple 7-designs,automorphism group ptl,graph isomorphism,graph theory,group theory
Graph theory,Graph canonization,Graph automorphism,Linear algebra,Discrete mathematics,Combinatorics,Graph isomorphism,Graph property,Graph homomorphism,Isomorphism,Mathematics
Conference
ISBN
Citations 
PageRank 
3-540-60114-7
8
0.96
References 
Authors
8
5
Name
Order
Citations
PageRank
Anton Betten17014.96
Adalbert Kerber26310.89
Axel Kohnert311412.60
Reinhard Laue4345.17
Alfred Wassermann512523.33