Symplectic groups, symmetric designs, and line ovals
نویسندگان
چکیده
منابع مشابه
Symplectic Groups, Symmetric Designs, and Line Ovals*
Let I7 = Sp(2m, 2) and I’ = X7, where Z is the translation group of the affine space AG(2m, 2). 17 acts 2-transitively on the cosets of each orthogonal subgroup G@(2m, 2), E = *l, and r has a second class of subgroups isomorphic to 17 ([lo, pp. 236, 2401, [6], and [14]). By considering a certain symmetric design P(2m) having r as its full automorphism group, we will prove these results. The sym...
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A symplectic spread of a 2n-dimensional vector space V over GFðqÞ is a set of q þ 1 totally isotropic n-subspaces inducing a partition of the points of the underlying projective space. The corresponding translation plane is called symplectic. We prove that a translation plane of even order is symplectic if and only if it admits a completely regular line oval. Also, a geometric characterization ...
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In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of Niho bent functions and of their duals, we give explicit formula for the dual bent function and present direct connections with ovals and line ovals. We also...
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Let S be a compact Riemann surface without boundary. A symmetry of S is an anti-conformal, involutary automorphism. The xed point set of is a disjoint union of circles, each of which is called an oval of . A method is presented for counting the ovals of a symmetry when S admits a large group G of automorphisms, normalized by . The method involves only calculations in G, based on the geometric d...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1975
ISSN: 0021-8693
DOI: 10.1016/0021-8693(75)90130-1