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Lexicographically maximal edges of dual hypergraphs and Nash-solvability of tight game forms
We prove a new property of dual hypergraphs and derive from it Nash-solvability of the corresponding (tight) game forms. This result is known since...
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On those Boolean functions that are coset leaders of first order Reed-Muller codes
In this paper, we study the class of those Boolean functions that are coset leaders of first order Reed-Muller codes. We study their properties and...
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Critical Properties and Complexity Measures of Read-Once Boolean Functions
In this paper, we define a quasi-order on the set of read-once Boolean functions and show that this is a well-quasi-order. This implies that every...
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How Low can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Ω(log n ),...
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Hardness results for approximate pure Horn CNF formulae minimization
We study the hardness of approximation of clause minimum and literal minimum representations of pure Horn functions in n Boolean variables. We show...
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A non-cyclic triple-error-correcting BCH-like code and some minimum distance results
In this paper, we give the first example of a non-cyclic triple-error-correcting code which is not equivalent to the primitive BCH code. It has...
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Constructing differentially 4-uniform permutations over GF(22m ) from quadratic APN permutations over GF(22m+1)
In this paper, by means of the idea proposed by Carlet (ACISP 1-15,
2011 ), differentially 4-uniform permutations with the best known nonlinearity... -
Towards the classification of self-dual bent functions in eight variables
In this paper, we classify quadratic and cubic self-dual bent functions in eight variables with the help of computers. There are exactly four and 45...
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A construction of bent functions from plateaued functions
In this presentation, a technique for constructing bent functions from plateaued functions is introduced and analyzed. This generalizes earlier...
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A new construction of bent functions based on \({\mathbb{Z}}\) -bent functions
Dobbertin has embedded the problem of construction of bent functions in a recursive framework by using a generalization of bent functions called
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On CCZ-equivalence of addition mod 2 n
We show that addition mod 2 n is CCZ-equivalent to a quadratic vectorial Boolean function. We use this to reduce the solution of systems of...
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On the affine equivalence relation between two classes of Boolean functions with optimal algebraic immunity
Recently, two classes of Boolean functions with optimal algebraic immunity have been proposed by Carlet et al. and Wang et al., respectively....
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Geometric and design-theoretic aspects of semibent functions II
This article is the successor of Dempwolff and Neumann (Des. Codes Cryptogr. 57:373–381,
2010 ). We now consider semibent functions with a linear... -
Affine equivalence for rotation symmetric Boolean functions with 2 k variables
Rotation symmetric Boolean functions have been extensively studied in the last 10 years or so because of their importance in cryptography and coding...
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Counting all bent functions in dimension eight 99270589265934370305785861242880
Based on the classification of the homogeneous Boolean functions of degree 4 in 8 variables we present the strategy that we used to count the number...
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Relating three nonlinearity parameters of vectorial functions and building APN functions from bent functions
We survey the properties of two parameters introduced by C. Ding and the author for quantifying the balancedness of vectorial functions and of their...
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Geometric and design-theoretic aspects of semibent functions I
The two parts of this paper consider combinatorial and geometric aspects of semibent functions. In the first part of this note we obtain 2-designs...