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A recursive construction for new symmetric designs. (English) Zbl 1066.05029

Summary: We introduce a recursive construction of regular Hadamard matrices with row sum \(2h\) for \(h = \pm 3^{n}\). Whenever \(q = (2h-1)^{2}\) is a prime power, we construct, for every positive integer \(m\), a symmetric designs with parameters (\(4h^{2} (q^{m+1} - 1)/(q-1)\), \((2h^{2} - h)q^{m}\), \((h^{2}-h)q^{m}\)).

MSC:

05B05 Combinatorial aspects of block designs
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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[2] The CRC Handbook of Combinatorial Designs, C.J. Colbourn and J.H. Dinitz (eds), CRC Press (1996). · Zbl 0836.00010
[4] Y. J. Ionin, New symmetric designs from regular Hadamard matrices, The Electronic Journal of Combinatorics, Vol. 5 (1998), R1. · Zbl 0885.05020
[7] H. Kharaghani, On the twin designs with the Ionin-type parameters, The Electronic Journal of Combinatorics, Vol. 7 (2000) R1. · Zbl 0944.05013
[8] H. Kharaghani, On the Siamese twin designs, in: Finite Fields and Applications, D. Jungnickel and H. Niederreiter (eds), Springer-Verlag, Berlin, Heidelberg (2001) pp. 303-312. · Zbl 0976.05010
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