Partial difference sets from quadratic forms and $p$-ary weakly regular bent functions
Tao Feng, Bin Wen, Qing Xiang, Jianxing Yin · arXiv (Cornell University) · 2010
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.