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- W3083032059 abstract "In 2011, Penttila and Williford constructed an infinite new family of primitive $Q$-polynomial 3-class association schemes, not arising from distance regular graphs, by exploring the geometry of the lines of the unitary polar space $H(3,q^2)$, $q$ even, with respect to a symplectic polar space $W(3,q)$ embedded in it. In a private communication to Penttila and Williford, H.~Tanaka pointed out that these schemes have the same parameters as the 3-class schemes found by Hollmann and Xiang in 2006 by considering the action of $mathrm{PGL}(2,q^2)$, $q$ even, on a non-degenerate conic of $mathrm{PG}(2,q^2)$ extended in $mathrm{PG}(2,q^4)$. Therefore, the question arises whether the above association schemes are isomorphic. In this paper we provide the positive answer. As by product, we get an isomorphism of strongly regular graphs." @default.
- W3083032059 created "2020-09-11" @default.
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- W3083032059 date "2020-09-07" @default.
- W3083032059 modified "2023-10-16" @default.
- W3083032059 title "On the isomorphism of certain primitive $Q$-polynomial not $P$-polynomial association schemes" @default.
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