engleski

Some symmetric (47, 23, 11) designs

Up to isomorphism there are precisely fifty-four symmetric designs with parameters (47, 23, 11) admitting a faithful action of a Frobenius group of order 55. From these fifty-four designs one can construct 179 pairwise nonisomorphic 2-(23, 11, 10) designs as derived and 191 pairwise nonisomorphic 2-(24, 12, 11) designs as residual designs. We have determined full automorphism groups of all constructed designs. One of 2-(24, 12, 11) designs has full automorphism group of order 15840, isomorphic to the group $M_{; ; 11}; ; \times Z_{; ; 2}; ; $, acting transitively on the set of points.

Symmetric design; Hadamard Design; orbit structure; automorphism group; Mathieu group

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