Bent and vectorial bent functions, partial difference sets, and strongly regular graphs
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Tarih
2018
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Amer Inst Mathematical Sciences-Aims
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Bent and vectorial bent functions have applications in cryptography and coding and are closely related to objects in combinatorics and finite geometry, like difference sets, relative difference sets, designs and divisible designs. Bent functions with certain additional properties yield partial difference sets of which the Cayley graphs are always strongly regular. In this article we continue research on connections between bent functions and partial difference sets respectively strongly regular graphs. For the first time we investigate relations between vectorial bent functions and partial difference sets. Remarkably, properties of the set of the duals of the components play here an important role. Seeing conventional bent functions as 1-dimensional vectorial bent functions, some earlier results on strongly regular graphs from bent functions follow from our more general results. Finally we describe a recursive construction of infinitely many partial difference sets with a secondary construction of p-ary bent functions.
Açıklama
Cesmelioglu, Ayca/0000-0001-5049-9135
Anahtar Kelimeler
Bent Function, Vectorial Boolean Function, Partial Difference Set, Strongly Regular Graph, Dual Bent Function, Walsh Transform
Kaynak
Advances in Mathematics of Communications
WoS Q Değeri
Q3
Scopus Q Değeri
Q1
Cilt
12
Sayı
4
