Title

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

Document Type

Article

Publication Date

5-1-2009

Abstract

We prove that every polarity of PG(2k - 1,q), where k≥ 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to, PGk (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. © 2008 Springer Science+Business Media, LLC.

Publication Title

Designs, Codes, and Cryptography

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