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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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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.