A class of Siamese twin Menon designs
نویسنده
چکیده
A {0,±1}-matrix S is called a Siamese twin design sharing the entries of I, if S = I +K − L, where I,K,L are non-zero {0, 1}-matrices and both I + K and I + L are incidence matrices of symmetric designs with the same parameters. Let p and 2p−1 be prime powers and p ≡ 3 (mod 4). We describe a construction of a Siamese twin Menon design with parameters (4p, 2p − p, p − p), yielding a Siamese twin Hadamard design with parameters (4p − 1, 2p − 1, p − 1).
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Let p and 2p − 1 be prime powers and p ≡ 3 (mod 4). We describe a construction of a series of Siamese twin designs with Menon parameters (4p, 2p − p, p − p) intersecting in a derived design with parameters (2p − p, p − p, p − p − 1), and a pairwise balanced design PBD(2p − p, {p, p − p}, p − p − 1). When p and 2p − 1 are primes, the derived design and the pairwise balanced design are cyclic. Fu...
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