Paper Info
Title
Hadamard 2-(63,31,15) designs invariant under the dihedral group of order 10
Abstract
ll Hadamard 2-(63,31,15) designs invariant under the dihedral group of order 10 are constructed and classified up to isomorphism together with related Hadamard matrices of order 64. Affine 2-(64,16,5) designs can be obtained from Hadamard 2-(63,31,15) designs having line spreads by Rahilly's construction [A. Rahilly, On the line structure of designs, Discrete Math. 92 (1991) 291-303]. The parameter set 2-(64,16,5) is one of two known sets when there exists several nonisomorphic designs with the same parameters and p-rank as the design obtained from the points and subspaces of a given dimension in affine geometry AG(n,p^m) (p a prime). It is established that an affine 2-(64,16,5) design of 2-rank 16 that is associated with a Hadamard 2-(63,31,15) design invariant under the dihedral group of order 10 is either isomorphic to the classical design of the points and hyperplanes in AG(3,4), or is one of the two exceptional designs found by Harada, Lam and Tonchev [M. Harada, C. Lam, V.D. Tonchev, Symmetric (4, 4)-nets and generalized Hadamard matrices over groups of order 4, Designs Codes Cryptogr. 34 (2005) 71-87].
Year
DOI
Venue
2009
10.1016/j.disc.2008.02.001
Discrete Mathematics
Keywords
Field
DocType
hadamard matrix,line spread,automorphism,hadamard design,classification,dihedral group
Hadamard's maximal determinant problem,Discrete mathematics,Affine geometry,Combinatorics,Hadamard matrix,Dihedral group,Hadamard three-lines theorem,Invariant (mathematics),Hadamard's inequality,Hadamard transform,Mathematics
Journal
Volume
Issue
ISSN
309
6
Discrete Mathematics
Citations 
PageRank 
References 
0
0.34
15
Authors
2
Name
Order
Citations
PageRank
Zlatka Mateva100.34
Svetlana Topalova2258.30