Parallel Class Intersection Matrices of Orthogonal Resolutions

Zhelezova, Stela. "Parallel Class Intersection Matrices of Orthogonal Resolutions." Serdica Journal of Computing 2.4 (2008): 321-330. <http://eudml.org/doc/11470>.

@article{Zhelezova2008,
abstract = {This work was partially supported by the Bulgarian National Science Fund under Contract No MM 1405. Part of the results were announced at the Fifth International Workshop on Optimal Codes and Related Topics (OCRT), White Lagoon, June 2007, BulgariaParallel class intersection matrices (PCIMs) have been defined and used in [6], [14], [15] for the classification of resolvable designs with several parameter sets. Resolutions which have orthogonal resolutions (RORs) have been classified in [19] for designs with some small parameters. The present paper deals with the additional restrictions that the existence of an orthogonal mate might impose on the PCIMs of a resolution, and with the effect of both PCIMs usage and the methods for RORs construction described in [19] and [20]. It is shown in several examples how consideration of PCIMs can result in constructing only of solutions which can have orthogonal mates, and thus substantially improve the computation time. There are parameters for which PCIMs make the classification of RORs possible, and also cases when PCIMs directly prove the nonexistence of doubly resolvable designs with certain parameters.},
author = {Zhelezova, Stela},
journal = {Serdica Journal of Computing},
keywords = {Classification; Resolvable Design; Orthogonal Resolution; classification; resolvable design; orthogonal resolution; parallel class intersection matrices; PCIM; orthogonal resolutions; ROR},
language = {eng},
number = {4},
pages = {321-330},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Parallel Class Intersection Matrices of Orthogonal Resolutions},
url = {http://eudml.org/doc/11470},
volume = {2},
year = {2008},
}

TY - JOUR
AU - Zhelezova, Stela
TI - Parallel Class Intersection Matrices of Orthogonal Resolutions
JO - Serdica Journal of Computing
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 2
IS - 4
SP - 321
EP - 330
AB - This work was partially supported by the Bulgarian National Science Fund under Contract No MM 1405. Part of the results were announced at the Fifth International Workshop on Optimal Codes and Related Topics (OCRT), White Lagoon, June 2007, BulgariaParallel class intersection matrices (PCIMs) have been defined and used in [6], [14], [15] for the classification of resolvable designs with several parameter sets. Resolutions which have orthogonal resolutions (RORs) have been classified in [19] for designs with some small parameters. The present paper deals with the additional restrictions that the existence of an orthogonal mate might impose on the PCIMs of a resolution, and with the effect of both PCIMs usage and the methods for RORs construction described in [19] and [20]. It is shown in several examples how consideration of PCIMs can result in constructing only of solutions which can have orthogonal mates, and thus substantially improve the computation time. There are parameters for which PCIMs make the classification of RORs possible, and also cases when PCIMs directly prove the nonexistence of doubly resolvable designs with certain parameters.
LA - eng
KW - Classification; Resolvable Design; Orthogonal Resolution; classification; resolvable design; orthogonal resolution; parallel class intersection matrices; PCIM; orthogonal resolutions; ROR
UR - http://eudml.org/doc/11470
ER -