Partial difference sets from quadratic forms and $p$-ary weakly regular bent functions

Details Partial difference sets from quadratic forms and $p$-ary weakly regular bent functions Partial difference sets from quadratic forms and $p$-ary weakly regular bent functions

2010-02-14

arxiv.org/abs/1002.2797v2

Mathematics

Combinatorics

17 pages. To apeear

Scientific paper

We generalize the construction of affine polar graphs in two different ways to obtain new partial difference sets and amorphic association schemes. The first generalization uses a combination of quadratic forms and uniform cyclotomy. In the second generalization we replace the quadratic form in the affine polar graph construction by higher degree homogeneous functions that are $p$-ary weakly regular bent. The negative Latin square type partial difference sets arising from the first generalization are new.

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