On affine designs and Hadamard designs with line spreads☆
Document Type
Article
Publication Date
7-2008
Abstract
Rahilly [On the line structure of designs, Discrete Math. 92 (1991) 291–303] described a construction that relates any Hadamard design H on 4m − 1 points with a line spread to an affine design having the same parameters as the classical design of points and hyperplanes in AG(m, 4). Here it is proved that the affine design is the classical design of points and hyperplanes in AG(m, 4) if, and only if, H is the classical design of points and hyperplanes in PG(2m−1, 2) and the line spread is of a special type. Computational results about line spreads in PG(5, 2) are given. One of the affine designs obtained has the same 2-rank as the design of points and planes in AG(3, 4), and provides a counter-example to a conjecture of Hamada [On the p-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error-correcting codes, Hiroshima Math. J. 3 (1973) 153–226].
Publication Title
Discrete Mathematics
Recommended Citation
Mavron, V. C.,
McDonough, T. P.,
&
Tonchev, V.
(2008).
On affine designs and Hadamard designs with line spreads☆.
Discrete Mathematics,
308(13), 2742-2750.
http://doi.org/10.1016/j.disc.2006.06.039
Retrieved from: https://digitalcommons.mtu.edu/math-fp/110
Publisher's Statement
© 2007 Elsevier B.V. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.disc.2006.06.039