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Some New Bush-Type Hadamard Matrices of Order 100 and Infinite Classes of Symmetric Designs

There are at least 52432 symmetric (100, 45, 20) designs on which Frob_{;10}; x Z_2 acts as an automorphism group. All these designs correspond to Bush-type Hadamard matrices of order 100, and each leads to an infinite class of twin designs with parameters v=100(81^m+81^{;m-1};+ \cdots +81+1), \ k=45(81)^m, \ \lambda=20(81)^m, and an infinite class of Siamese twin designs with parameters v=100(121^m+121^{;m-1};+ \cdots +121+1), \ k=55(121)^m, \ \lambda=30(121)^m, where m is an arbitrary positive integer. One of the constructed designs is isomorphic to that used by Z. Janko, H. Kharaghani and V. D. Tonchev [1]. REFERENCES: Z. Janko, H. Kharaghani, V. D. Tonchev, Bush-Type Hadamard Matrices and Symmetric Designs, J. Combin Designs 9: 72--78, 2001.

symmetric design; Bush-type Hadamard matrix; automorphism group; generalized weighing matrix

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