Abstract
Let 4n 2 be the order of a Bush-type Hadamard matrix with q = (2n + 1)2 a prime power. It is shown that there is a weighing matrix
which can be used to construct a pair of symmetric designs with the parameters
for every positive integer m. As a corollary we get a new class of symmetric designs with parameters
for all positive integers m and n, where 4n is the order a Hadamard matrix.
Thanks to W. Holzmann for his help and useful conversation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K.A. Bush: Unbalanced Hadamard matrices and finite projective planes of even order, JCT, 11(1971), pp. 38–44.
Frans C. Bussemaker, Willem Haemers and Edward Spence: The search for pseudo orthogonal Latin squares of order six, preprint.
Warwick de Launey: Section on “Bhaskar Rao designs,” CRC Handbook of Combinatorial Designs, edited by Charles J. Colbourn and Jeffrey H. Dinitz, Kluwer Academic Press, 1996.
Dieter Jungnickel and Vladimir Tonchev: Perfect Codes and Balanced Weighing Matrices, To appear (1999).
Zvonimir Janko, Hadi Kharaghani and Vladimir D. Tonchev, The existence of a Bush-type Hadamard matrix of order 324 and two new infinite classes of symmetric designs, preprint.
Y.J. Ionin: New symmetric designs from regular Hadamard matrices. The Electronic Journal of Combinatorics, Vol. 5, No.1 (1998), R1.
H. Kharaghani: On the twin designs with the Ionin-type parameters. The Electronic Journal of Combinatorics, (2000), #R1.
H. Kharaghani: New classes of weighing matrices, ARS comb., 19(1985), pp. 69–72.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kharaghani, H. (2001). On the Siamese Twin Designs. In: Jungnickel, D., Niederreiter, H. (eds) Finite Fields and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56755-1_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-56755-1_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62498-8
Online ISBN: 978-3-642-56755-1
eBook Packages: Springer Book Archive