There are infinitely many bent functions for which the dual is not bent
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Dosyalar
Tarih
2016
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Ieee-Inst Electrical Electronics Engineers Inc
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and non-weakly regular bent functions. Regular and weakly regular bent functions always appear in pairs, since their duals are also bent functions. In general, this does not apply to non-weakly regular bent functions. However, the first known construction of non-weakly regular bent functions by Cesmelioglu et al. yields bent functions for which the dual is also bent. In this paper, the first construction of non-weakly regular bent functions for which the dual is not bent is presented. We call such functions nondual-bent functions. Until now, only sporadic examples found via computer search were known. We then show that with the direct sum of bent functions and with the construction by Cesmelioglu et al., one can obtain infinitely many non-dual-bent functions once one example of a non-dual-bent function is known.
Açıklama
Cesmelioglu, Ayca/0000-0001-5049-9135
Anahtar Kelimeler
Bent Function, Dual, Walsh Transform, Vectorial Function, Non-Weakly Regular
Kaynak
Ieee Transactions on Information Theory
WoS Q Değeri
Q3
Scopus Q Değeri
Q1
Cilt
62
Sayı
9
