engleski

Constructing a Multiple Series of Hadamard Designs

Combining the ideas of constructing symmetric designs assuming an action of an automorphism group acting on them, together with the theoretical approach of calculations in the finite field GR(l), we are able to construct a multiple series of Hadamard designs with parameters (4l+3, 2l+1, l), for every l being an odd prime power. If l = 3 (mod 4), then we show that there are 54 examples of such Hadamard designs and if l = 1 (mod 4), then there are always 3 examples of Hadamard designs. They all admit an action of a group isomorphic to the semidirect product of the elementary abelian group of order l with the cyclic group of order (l-1)/2.

Hadamard design; automorphism group; tactical decomposition

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