Strongly regular graphs arising from non-weakly regular bent functions


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ÖZBUDAK F. , PELEN R. M.

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, cilt.11, ss.1297-1306, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 11 Konu: 6
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s12095-019-00394-2
  • Dergi Adı: CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
  • Sayfa Sayıları: ss.1297-1306

Özet

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.