Polarities, quasi-symmetric designs, and Hamada's conjecture
Document Type
Article
Publication Date
5-2009
Department
Department of Mathematical Sciences
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.
Publication Title
Designs, Codes, and Cryptography
Recommended Citation
Jungnickel, D.,
&
Tonchev, V.
(2009).
Polarities, quasi-symmetric designs, and Hamada's conjecture.
Designs, Codes, and Cryptography,
51(2), 131-140.
http://doi.org/10.1007/s10623-008-9249-8
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4874
