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On Point-Cyclic Resolutions of the 2-(63,7,15) Design Associated with PG(5,2)
Graphs and Combinatorics (2002)
  • Jumela F Sarmiento, Kyushu University
Abstract
A t(v,k,λ) design is a set of v points together with a collection of its k-subsets called blocks so that t points are contained in exactly λ blocks. PG(n,q), the n-dimensional projective geometry over GF(q) is a 2(q n+q n−1+⋯+q+1,q 2+q+1, q n−2+ q n−3+⋯+q+1) design when we take its points as the points of the design and its planes as the blocks of the design. A 2(v,k,λ) design is said to be resolvable if the blocks can be partitioned as ℱ={R 1,R 2,…,R s }, where s=λ(v−1)/(k−1) and each R i consists of v/k disjoint blocks. If a resolvable design has an automorphism σ which acts as a cycle of length v on the points and ℱσ=ℱ, then the design is said to be point-cyclically resolvable. The design consisting of points and planes of PG(5,2) is shown to be point-cyclically resolvable by enumerating all inequivalent resolutions which are invariant under a cyclic automorphism group G=〈σ〉 where σ is a cycle of length v. These resolutions are shown to be the only resolutions which admit point-transitive automorphism group.
Keywords
  • Automorphism Group,
  • Projective Geometry,
  • Resolvable Design,
  • Cyclic Automorphism,
  • Design Associate
Publication Date
October, 2002
DOI
https://doi.org/10.1007/s003730200046
Citation Information
Sarmiento, J. F. (2002). On Point-Cyclic Resolutions of the 2-(63,7,15) Design Associated with PG(5,2). Graphs and Combinatorics, 18(3), 621–632. https://doi.org/10.1007/s003730200046