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- W2039770337 abstract "By modifying a construction for Hadamard (Menon) difference sets we construct two infinite families of negative Latin square type partial difference sets in groups of the form $${mathbb {Z}_3^2 times mathbb {Z}_p^{4t}}$$ where p is any odd prime. One of these families has the well-known Paley parameters, which had previously only been constructed in p-groups. This provides new constructions of Hadamard matrices and implies the existence of many new strongly regular graphs including some that are conference graphs. As a corollary, we are able to construct Paley–Hadamard difference sets of the Stanton-Sprott family in groups of the form $${mathbb {Z}_3^2 times mathbb {Z}_p^{4t} times {it EA} (9p^{4t} pm 2)}$$ when $${9p^{4t} pm 2}$$ is a prime power. These are new parameters for such difference sets." @default.
- W2039770337 created "2016-06-24" @default.
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- W2039770337 date "2009-02-18" @default.
- W2039770337 modified "2023-09-26" @default.
- W2039770337 title "Paley type partial difference sets in non p-groups" @default.
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- W2039770337 doi "https://doi.org/10.1007/s10623-009-9274-2" @default.
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