Elsevier

Discrete Mathematics

Volumes 106–107, 1 September 1992, Pages 19-23
Discrete Mathematics

Cyclic affine planes and Paley difference sets

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Abstract

The existence of a cyclic affine plane implies the existence of a Paley type difference set. We use the existence of this difference set to give the following condition on the existence of cyclic affine planes of order n: If n ≡ 8 mod 16 then n − 1 must be a prime. We discuss the structure of the Paley type difference set constructed from the plane.

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Research partially supported by NSA grant MDA 904-90-H-4008 and by an Alexander-von-Humboldt fellowship. The author thanks the mathematisches Institut der Universität Gieβen for its hospitality during the time of this research.