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Essential Arity Gap of Boolean Functions

Shtrakov, Slavcho (2008)

Serdica Journal of Computing

In this paper we investigate the Boolean functions with maximum essential arity gap. Additionally we propose a simpler proof of an important theorem proved by M. Couceiro and E. Lehtonen in [3]. They use Zhegalkin’s polynomials as normal forms for Boolean functions and describe the functions with essential arity gap equals 2. We use to instead Full Conjunctive Normal Forms of these polynomials which allows us to simplify the proofs and to obtain several combinatorial results concerning the Boolean functions...

Estudio de algunas secuencias pseudoaleatorias de aplicación criptográfica.

P. Caballero Gil, A. Fúster Sabater (1998)

Revista Matemática Complutense

Pseudorandom binary sequences are required in stream ciphers and other applications of modern communication systems. In the first case it is essential that the sequences be unpredictable. The linear complexity of a sequence is the amount of it required to define the remainder. This work addresses the problem of the analysis and computation of the linear complexity of certain pseudorandom binary sequences. Finally we conclude some characteristics of the nonlinear function that produces the sequences...

Explicit form for the discrete logarithm over the field GF ( p , k )

Gerasimos C. Meletiou (1993)

Archivum Mathematicum

For a generator of the multiplicative group of the field G F ( p , k ) , the discrete logarithm of an element b of the field to the base a , b 0 is that integer z : 1 z p k - 1 , b = a z . The p -ary digits which represent z can be described with extremely simple polynomial forms.

Exploring invariant linear codes through generators and centralizers

Partha Pratim Dey (2005)

Archivum Mathematicum

We investigate a H -invariant linear code C over the finite field F p where H is a group of linear transformations. We show that if H is a noncyclic abelian group and ( | H | , p ) = 1 , then the code C is the sum of the centralizer codes C c ( h ) where h is a nonidentity element of H . Moreover if A is subgroup of H such that A Z q × Z q , q p , then dim  C is known when the dimension of C c ( K ) is known for each subgroup K 1 of A . In the last few sections we restrict our scope of investigation to a special class of invariant codes, namely affine...

Exponential entropy on intuitionistic fuzzy sets

Rajkumar Verma, Bhu Dev Sharma (2013)

Kybernetika

In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov's intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some interesting properties of this measure are analyzed. Finally, a numerical example is given to show that...

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