Designs with the symmetric difference property on 64 points and their groups

Christopher Parker; Edward Spence; Vladimir D. Tonchev

doi:10.1016/0097-3165(94)90002-7

Designs with the symmetric difference property on 64 points and their groups

Christopher Parker^*, Edward Spence, Vladimir D. Tonchev

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The automorphism groups of the symmetric 2-(64, 28, 12) designs with the symmetric difference property (SDP), as well as the groups of their derived and residual designs, are computed. The symmetric SDP designs all have transitive automorphism groups. In addition, they all admit transitive regular subgroups, or equivalently, (64, 28, 12) difference sets. These results are used for the enumeration of certain binary codes achieving the Grey-Rankin bound and point sets of elliptic or hyperbolic type in PG(5, 2).

Original language	English
Pages (from-to)	23-43
Number of pages	21
Journal	Journal of Combinatorial Theory, Series A
Volume	67
Issue number	1
DOIs	https://doi.org/10.1016/0097-3165(94)90002-7
Publication status	Published - Jul 1994

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0097-3165(94)90002-7

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abstract = "The automorphism groups of the symmetric 2-(64, 28, 12) designs with the symmetric difference property (SDP), as well as the groups of their derived and residual designs, are computed. The symmetric SDP designs all have transitive automorphism groups. In addition, they all admit transitive regular subgroups, or equivalently, (64, 28, 12) difference sets. These results are used for the enumeration of certain binary codes achieving the Grey-Rankin bound and point sets of elliptic or hyperbolic type in PG(5, 2).",

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Designs with the symmetric difference property on 64 points and their groups

Abstract

ASJC Scopus subject areas

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