Symplectic Groups, Symplectic Spreads, Codes, and Unimodular Lattices
نویسندگان
چکیده
منابع مشابه
Symplectic Spreads
We construct an infinite family of symplectic spreads in spaces of odd rank and characteristic.
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If π is a finite symplectic translation plane, it is shown that any affine homology group is cyclic and has order dividing the order of the kernel homology group. This criterion provides a means to ensure that a given spread is not symplectic. Furthermore, a variety of symplectically paired André spreads are constructed.
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Every symplectic spread of PG(3, q), or equivalently every ovoid of Q(4, q), is shown to give a certain family of permutation polynomials of GF (q) and conversely. This leads to an algebraic proof of the existence of the Tits-Lüneburg spread of W (2) and the Ree-Tits spread of W (3), as well as to a new family of low-degree permutation polynomials over GF (3). Let PG(3, q) denote the projective...
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Commutative semifields are constructed by using their relationship with symplectic spreads. The number of pairwise nonisomorphic commutative semifield planes of even order N obtained in this manner is not bounded above by any polynomial in N . The number previously known for any N was less than logN . 2003 Elsevier Inc. All rights reserved. MSC: primary 51A40, 17A35; secondary 05B25, 51A35, 5...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1997
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6902