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arXiv · 0704.2203

On Abelian Difference Sets with Parameters of 3-dimensional Projective Geometries

Kevin Jennings
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Abstract

A difference set is said to have classical parameters if $ (v,k, λ) = (\frac{q^d-1}{q-1}, \frac{q^{d-1}-1}{q-1}, \frac{q^{d-2}-1}{q-1}).$ The case $d=3$ corresponds to planar difference sets. We focus here on the family of abelian difference sets with $d=4$. The only known examples of such difference sets correspond to the projective geometries $PG(3,q)$. We consider an arbitrary difference set with the parameters of $PG(3,q)$ in an abelian group and establish constraints on its structure. In particular, we discern embedded substructures.

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Kevin Jennings. 2007-04-17. On Abelian Difference Sets with Parameters of 3-dimensional Projective Geometries. https://arxiv.org/abs/0704.2203

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