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Some Hadamard designs admitting a faithful action of Frobenius groups

We have constructed three new symmetric (71, 35, 17) designs having $Frob_{17 \cdot 8}$ as an automorphism group. Also constructed are symmetric designs with parameters (43, 21, 10), (67, 33, 16) and (71, 35, 17) admitting an automorphism group isomorphic to $Frob_{43 \cdot 7}$, $Frob_{67 \cdot 11}$ and $Frob_{71 \cdot 7}$, respectively, which turn out to be isomorphic to previously known designs, constructed via cyclic difference sets. Each constructed Hadamard design leads to a series of Hadamard designs.

symmetric design; Hadamard design; Frobenius group; automorphism group

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