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Cryptography and Communications

Erschienen in:

14.09.2019

Strongly regular graphs arising from non-weakly regular bent functions

verfasst von: Ferruh Özbudak, Rumİ Melİh Pelen

Erschienen in: Cryptography and Communications | Ausgabe 6/2019

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Abstract

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 Çesmelioğlu 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.

Vorheriger Artikel Frobenius linear translators giving rise to new infinite classes of permutations and bent functions

Nächster Artikel Image sets with regularity of differences

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Titel: Strongly regular graphs arising from non-weakly regular bent functions
verfasst von: Ferruh Özbudak
Rumİ Melİh Pelen
Publikationsdatum: 14.09.2019
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 6/2019
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-019-00394-2

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