Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Journal of Computing, Vol. 2, No 4, (2008), 321p-330p
Abstract:
Parallel 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.
Description:
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, Bulgaria
