Strongly regular graphs arising from non-weakly regular bent functions

Date

2019-11-01

Author

Özbudak, Ferruh

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In this paper, we study two special subsets of a finite field of odd characteristics associated with non-weakly regular bent functions. We show that those subsets associated to non-weakly regular even bent functions in the GMMF class (see cesmelioglu et al. Finite Fields Appl. 24, 105-117 2013) are never partial difference sets (PDSs), and are PDSs if and only if they are trivial subsets. Moreover, we analyze the two known sporadic examples of non-weakly regular ternary bent functions given in Helleseth and Kholosha (IEEE Trans. Inf. Theory 52(5), 2018-2032 2006, Cryptogr. Commun. 3(4), 281-291 2011). We observe that corresponding subsets are non-trivial partial difference sets. We show that they are the union of some cyclotomic cosets and so correspond to 2-class fusion schemes of a cyclotomic scheme. We also present a further construction giving non-trivial PDSs from certain p-ary functions which are not bent functions.

Subject Keywords

Computer Networks and Communications, Computational Theory and Mathematics, Applied Mathematics

URI

https://hdl.handle.net/11511/37529

Journal

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES

DOI

https://doi.org/10.1007/s12095-019-00394-2

Collections

Department of Mathematics, Article

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Citation Formats

F. Özbudak, “Strongly regular graphs arising from non-weakly regular bent functions,” CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, pp. 1297–1306, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37529.