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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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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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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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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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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... -
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... -
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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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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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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Some general properties of modified bent functions through addition of indicator functions
Properties of a secondary bent function construction that adds the indicator of an affine subspace of arbitrary dimension to a given bent function in n ...
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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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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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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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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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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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Bent functions in the partial spread class generated by linear recurring sequences
We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the...
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Results on the nonexistence of bent-negabent rotation symmetric Boolean functions
In this paper, we study the conjecture that there doesn’t exist bent-negabent rotation symmetric Boolean functions. We prove that the conjecture is...