New Distance Regular Graphs Arising from Dimensional Dual Hyperovals
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In 4 we have studied the semibiplanes ?m,he=Af(Sm,he) obtained as affine expansions of the d -dimensional dual hyperovals of Yoshiara 6. We continue that investigation here, but from a graph theoretic point of view. Denoting by?m, he the incidence graph of (the point-block system of)?m, he, we prove that ?m,heis distance regular if and only if eitherm+h=e or (m+h,e ) = 1. In the latter case, ?m,hehas the same array as the coset graph Kheof the extended binary Kasami code K(2e, 2h) but, as we prove in this paper, we have ?m, he ~ =Kheif and only if m=h. Finally, by exploiting some information obtained on ?m, he, we prove that if e? 13 and m?=h with (m+h, e) = 1, then ?m,heis simply connected.
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