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A further study on the construction methods of bent functions and self-dual bent functions based on Rothaus’s bent function
Bent functions are maximally nonlinear Boolean functions. They are important functions introduced by Rothaus and studied firstly by Dillon and next...
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Decomposing self-dual bent functions
Bent functions are Boolean functions in even number of variables that have maximal nonlinearity. They have flat Walsh–Hadamard spectrum and are of...
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Derivatives of bent functions in connection with the bent sum decomposition problem
In this paper, we investigate when a balanced function can be a derivative of a bent function. We prove that every nonconstant affine function in an...
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Look into the Mirror: Evolving Self-dual Bent Boolean Functions
Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such... -
Generalized partially bent functions, generalized perfect arrays, and cocyclic Butson matrices
In a recent survey, Schmidt compiled equivalences between generalized bent functions, group invariant Butson Hadamard matrices, and abelian splitting...
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Semantic mutation operator for a fast and efficient design of bent Boolean functions
Boolean functions are important cryptographic primitives with extensive use in symmetric cryptography. These functions need to possess various...
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Several secondary methods for constructing bent–negabent functions
In this paper, we present three secondary methods for constructing bent–negabent functions under the frameworks of the indirect sum construction...
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New Classes of Bent Functions via the Switching Method
The switching method is a powerful method to construct bent functions. In this paper, using this method, we present two generic constructions of... -
Explicit infinite families of bent functions outside the completed Maiorana–McFarland class
During the last five decades, many different secondary constructions of bent functions were proposed in the literature. Nevertheless, apart from a...
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On the higher-order nonlinearity of a new class of biquadratic Maiorana–McFarland type bent functions
In 1974, Dillon introduced two significant classes of bent functions, namely the Maiorana–McFarland class and the Partial Spread class. In this...
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Quadratic bent functions and their duals
We obtain geometric characterizations of the dual functions for quadratic bent and vectorial bent functions in terms of quadrics. Additionally, using...
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Vectorial bent functions and linear codes from quadratic forms
In this paper, we study the vectorial bentness of an arbitrary quadratic form and construct two classes of linear codes of few weights from the...
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Several classes of bent functions over finite fields
Inspired by the works of Mesnager (IEEE Trans Inf Theory 60(7):4397–4407, 2014) and Tang et al. (IEEE Trans Inf Theory 63(10):6149–6157, 2017), we...
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Vectorial Boolean functions with the maximum number of bent components beyond the Nyberg’s bound
Recently, several interesting constructions of vectorial Boolean functions with the maximum number of bent components (MNBC functions, for short)...
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Heuristic search of (semi-)bent functions based on cellular automata
An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions : given a known...
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Ternary self-orthogonal codes from weakly regular bent functions and their application in LCD Codes
Self-orthogonal codes are linear codes such that they are contained in their duals. Self-orthogonal codes have attracted much attention due to their...
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A survey on p-ary and generalized bent functions
Boolean bent functions have been introduced by Rothaus in 1966, bent functions in odd characteristic were first considered in 1985 by Kumar, Scholtz,...
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Constructing new superclasses of bent functions from known ones
Some recent research articles (Zhang et al. in Lecture Notes in Computer Science, 10194, 298-313. (
2017 ), Zhang et al. in Discret. Appl. Math....