Geodesic
Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs
Serdica Journal of Computing, Tome 2 (2008) no. 4, pp. 349-368

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

The author developed computer programs needed for the classification of designs with certain automorphisms by the local approach method. All these programs use canonicity test or/and construction of canonical form of an integer matrix. Their efficiency substantially influences the speed of the whole computation. The present paper deals with the implemented canonicity algorithm. It is based on ideas used by McKay, Meringer, Kaski and Bouyukliev, but while their algorithms are for the equivalence test, the canonicity test or finding canonical representative of only one type of combinatorial object (graph, code, design, binary matrix, etc.), the algorithm presented in this paper is meant to work fast on all types of integer matrices used for the classification of designs with predefined automorphisms. This is achieved through the suitable spectrum invariant, and the way it is used to cut off some branches of the search tree.
Keywords: Algorithm, Automorphism, Incidence Matrix, Orbit Matrix, Group Action, Canonical Form, BIBD 
@article{SJC_2008_2_4_a3,
     author = {Mateva, Zlatka},
     title = {Constructing a {Canonical} form of a {Matrix} in {Several} {Problems} about {Combinatorial} {Designs}},
     journal = {Serdica Journal of Computing},
     pages = {349--368},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJC_2008_2_4_a3/}
}
TY  - JOUR
AU  - Mateva, Zlatka
TI  - Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs
JO  - Serdica Journal of Computing
PY  - 2008
SP  - 349
EP  - 368
VL  - 2
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJC_2008_2_4_a3/
LA  - en
ID  - SJC_2008_2_4_a3
ER  - 
%0 Journal Article
%A Mateva, Zlatka
%T Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs
%J Serdica Journal of Computing
%D 2008
%P 349-368
%V 2
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJC_2008_2_4_a3/
%G en
%F SJC_2008_2_4_a3
Mateva, Zlatka. Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs. Serdica Journal of Computing, Tome 2 (2008) no. 4, pp. 349-368. http://geodesic.mathdoc.fr/item/SJC_2008_2_4_a3/