کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4655795 | 1343404 | 2011 | 9 صفحه PDF | دانلود رایگان |
In a recent paper, two of the authors used polarities in PG(2d−1,p) (p⩾2 prime, d⩾2) to construct non-geometric designs having the same parameters and the same p-rank as the geometric design PGd(2d,p) having as blocks the d-subspaces in the projective space PG(2d,p), hence providing the first known infinite family of examples where projective geometry designs are not characterized by their p-rank, as it is the case in all known proven cases of Hamada's conjecture. In this paper, the construction based on polarities is extended to produce designs having the same parameters, intersection numbers, and 2-rank as the geometric design AGd+1(2d+1,2) of the (d+1)-subspaces in the binary affine geometry AG(2d+1,2). These designs generalize one of the four non-geometric self-orthogonal 3-(32,8,7) designs of 2-rank 16 (V.D. Tonchev, 1986 [12]), and provide the only known infinite family of examples where affine geometry designs are not characterized by their rank.
Journal: Journal of Combinatorial Theory, Series A - Volume 118, Issue 1, January 2011, Pages 231-239