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Polynomial Criterion for Abelian Difference Sets
Indian Journal of Pure and Applied Mathematics ( IF 0.7 ) Pub Date : 2020-03-13 , DOI: 10.1007/s13226-020-0397-5
Pradipkumar H. Keskar , Priyanka Kumari

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.

中文翻译:

Abelian差异集的多项式准则

差异集是满足组操作某些组合属性的组子集。可以使用相应组的组环中的相等性来表征它们。在本文中,我们利用Abelian组的群环的特殊结构,建立该组中具有特定参数的差分集与指定多项式系统的所有复数解的一一对应关系方程。该对应关系还开发了一些将布尔函数变为折弯函数的测试。
更新日期:2020-03-13
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