Polynomial Criterion for Abelian Difference Sets

Pradipkumar H. Keskar () and Priyanka Kumari ()
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Pradipkumar H. Keskar: Birla Intitute of Technology and Science, Pilani (Pilani Campus)
Priyanka Kumari: Birla Intitute of Technology and Science, Pilani (Pilani Campus)

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 233-249

Abstract: Abstract Difference sets are subsets of a group satisfying certain combinatorial property with respect to the group operation. They can be characterized using an equality in the group ring of the corresponding group. In this paper, we exploit the special structure of the group ring of an Abelian group to establish a one-to one correspondence of the class of difference sets with specific parameters in that group with the set of all complex solutions of a specified system of polynomial equations. The correspondence also develops some tests for a Boolean function to be a bent function.

Keywords: Difference set; group ring; point representation; ideal membership; bent function; 05B10; 11T71; 13P99 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0397-5

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