Polarities, quasi-symmetric designs, and Hamada's conjecture

被引：28

作者：

Jungnickel, Dieter ^{[1
]}

Tonchev, Vladimir D. ^{[2
]}

机构：

[1] Univ Augsburg, Lehrstuhl Diskrete Math Optimierung & Operat Res, D-86135 Augsburg, Germany

[2] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2009年 / 51卷 / 02期

关键词：

Polarity; Projective geometry; Design; Quasi-symmetric design; Hamada's conjecture; HADAMARD DESIGNS; AFFINE DESIGNS; GOOD BLOCKS; MATRICES; NUMBER; CODES;

D O I：

10.1007/s10623-008-9249-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove that every polarity of PG(2k - 1,q), where ka parts per thousand yen 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to, PG (k) (2k,q). In particular, the case k = 2 yields a new family of quasi-symmetric designs. We also show that our construction provides an infinite family of counterexamples to Hamada's conjecture, for any field of prime order p. Previously, only a handful of counterexamples were known.

引用

页码：131 / 140

页数：10

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