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.
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Acknowledgement
Both the authors thank the support from FIST Programme vide SR/FST/MSI-090/2013 of DST, Govt. of India. The second author thanks UGC, Govt of India for the support under JRF Programme (SR. No. 2061540979, Ref. No. 21/06/2015(1)EU-V R. No. 426800). Both the authors thank S. Gangopadhyay and B. Mandal of IIT, Roorkee for stimulating discussions.
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Keskar, P.H., Kumari, P. Polynomial Criterion for Abelian Difference Sets. Indian J Pure Appl Math 51, 233–249 (2020). https://doi.org/10.1007/s13226-020-0397-5
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DOI: https://doi.org/10.1007/s13226-020-0397-5