engleski

Series of Menon designs, cyclic BIBDs and cyclic PBDs

Let $p$ and $2p-1$ be prime powers and $p \equiv 3\ (mod\ 4)$. We describe a construction of two Menon designs with parameters $(4p^2, 2p^2 - p, p^2 - p)$ which lead to amicable regular Hadamard matrices of order $4p^2$. These two Menon designs lead to a series of Siamese twin designs intersecting in a derived design with parameters $(2p^2-p, p^2-p, p^2-p-1)$, and a pairwise balanced design $PBD(2p^2-p, \{; ; ; ; p^2, p^2-p\}; ; ; ; , p^2-p-1)$. When $p$ and $2p-1$ are primes, the derived design and the pairwise balanced design are cyclic.

symmetric design; Hadamard matrix; cyclic design; pairwise balanced design

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