engleski

A Multiple Series of Hadamard Designs

On a series of Hadamard designs for (4l+3, 2l+1, l), we show how fruitful the method of tactical decompositions for symmmetric designs can be. We shall construct a multiple infinite series of such designs, for every l being an odd prime power. The existence of 3 non-isomorphic tactical decompositions shall be presented. Further, we shall prove our construction using the here possible calculations in the finite field GF(l). For every l which is a prime power, whenever l=3(mod 4), we get 54 non-isomorphic (4l+3, 2l+1, l) designs, while in the case of l=1(mod 4) we can get 3 Hadamard designs. All these designs admit an action of a semidirect product of cyclic groups of order l and (l-1)/2.

Hadamard design; tactical decomposition; finite field

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