Partial difference sets and amorphic group schemes from pseudo-quadratic bent functions
نویسندگان
چکیده
We present new abelian partial difference sets and amorphic group schemes of both Latin square type and negative Latin square type in certain abelian p-groups. Our method is to construct what we call pseudo-quadratic bent functions and use them in place of quadratic forms. We also discuss a connection between strongly regular bent functions and amorphic group schemes.
منابع مشابه
PARTIAL DIFFERENCE SETS FROM p-ARY WEAKLY REGULAR BENT FUNCTIONS AND QUADRATIC FORMS
We generalize the construction of affine polar graphs in two different ways to obtain partial difference sets and amorphic association schemes. In the first 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 second generalization uses a combination of quadratic forms and uniform cyclo...
متن کاملPartial Difference Sets from Quadratic Forms and p-ary Weakly Regular Bent Functions
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 regu...
متن کاملAmorphic association schemes with negative Latin square-type graphs
Applying results from partial difference sets, quadratic forms, and recent results of Brouwer and Van Dam, we construct the first known amorphic association scheme with negative Latin square type graphs and whose underlying set is a nonelementary abelian 2-group. We give a simple proof of a result of Hamilton that generalizes Brouwer’s result. We use multiple distinct quadratic forms to constru...
متن کاملNew negative Latin square type partial difference sets in nonelementary abelian 2-groups and 3-groups
A partial difference set having parameters (n2, r(n− 1), n+ r2 − 3r, r2 − r) is called a Latin square type partial difference set, while a partial difference set having parameters (n2, r(n+1),−n+r2+3r, r2+r) is called a negative Latin square type partial difference set. Nearly all known constructions of negative Latin square partial difference sets are in elementary abelian groups. In this pape...
متن کاملA construction of bent functions from plateaued functions
In this presentation a technique for constructing bent functions from plateaued functions is introduced. This generalizes earlier techniques for constructing bent from near-bent functions. Analysing the Fourier spectrum of quadratic functions we then can construct weakly regular as well as non-weakly regular bent functions both in even and odd dimension. This type of functions yield the first k...
متن کامل