Partial difference sets and amorphic group schemes from pseudo-quadratic bent functions

Authors:
Yu Qing Chen;John Polhill
Affiliations:
Department of Mathematics and Statistics, Wright State University, Dayton, USA 45435;Department of Mathematics, Computer Science, and Statistics, Bloomsburg University, Bloomsburg, USA 17815
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2013

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Abstract

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.