Automorphisms and isomorphisms of some p-ary bent functions
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DOI: 10.1007/s10801-019-00884-9
Abstract: In the predecessor to this paper Dempwolff (Comm Algebra 34(3):1077–1131, 2006), group-theoretic methods were used to solve automorphism and equivalence questions for (certain) ordinary bent functions, i.e., bent functions over $$\mathbb {F}_2$$F2. Here, we consider the… read more here.
Keywords: dempwolff comm; ary bent; algebra 1077; bent functions ... See more keywords
Fourier transforms on finite group actions and bent functions
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DOI: 10.1007/s10801-021-01057-3
Abstract: Highly nonlinear functions (bent functions, perfect nonlinear functions, etc.) on finite fields and finite (abelian or nonabelian) groups have been studied in numerous papers. As a generalization of bent functions on finite groups, bent functions… read more here.
Keywords: group; bent functions; functions finite; complex valued ... See more keywords
Classification and Construction of quaternary self-dual bent functions
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DOI: 10.1007/s12095-017-0216-y
Abstract: Quaternary self-dual bent functions are studied from the viewpoints of existence, construction, and symmetry. A search algorithm is described to classify their orbits under the orthogonal group in low dimensions. A connection with self-dual bent… read more here.
Keywords: quaternary self; construction; bent functions; self dual ... See more keywords
Several new classes of self-dual bent functions derived from involutions
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DOI: 10.1007/s12095-019-00371-9
Abstract: Bent functions are a kind of Boolean functions which have the maximum Hamming distance to linear and affine functions, they have some interesting applications in combinatorics, coding theory, cryptography and sequences. However, generally speaking, how… read more here.
Keywords: classes self; several new; bent functions; self dual ... See more keywords
Generic Construction of Bent Functions and Bent Idempotents With Any Possible Algebraic Degrees
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DOI: 10.1109/tit.2017.2717966
Abstract: As a class of optimal combinatorial objects, bent functions have important applications in cryptography, sequence design, and coding theory. Bent idempotents are a subclass of bent functions and of great interest, since they can be… read more here.
Keywords: construction bent; generic construction; bent functions; bent idempotents ... See more keywords
Further Results on Generalized Bent Functions and Their Complete Characterization
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DOI: 10.1109/tit.2018.2835518
Abstract: This paper contributes to increase our knowledge on generalized bent functions (including generalized bent Boolean functions and generalized $p$ -ary bent functions with odd prime $p$ ) by bringing new results on their characterization and… read more here.
Keywords: tex math; generalized bent; bent functions; inline formula ... See more keywords
On Design-Theoretic Aspects of Boolean and Vectorial Bent Function
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DOI: 10.1109/tit.2020.3040754
Abstract: There are two construction methods of designs from $(n,m)$ -bent functions, known as translation and addition designs. In this article we analyze, which equivalence relation for Boolean bent functions, i.e. $(n,1)$ -bent functions, and vectorial… read more here.
Keywords: tex math; inline formula; bent functions;
Relationship Between Homogeneous Bent Functions and Nagy Graphs
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DOI: 10.1134/s1990478919040173
Abstract: We study the relationship between homogeneous bent functions and some intersection graphs of a special type that are called Nagy graphs and denoted by Γ(n,k). The graph Γ(n,k) is the graph whose vertices correspond to… read more here.
Keywords: homogeneous bent; nagy graphs; bent functions; relationship homogeneous ... See more keywords