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Colouring of cycles in the de Bruijn graphs

Ewa Łazuka, Jerzy Żurawiecki (2000)

Discussiones Mathematicae Graph Theory

We show that the problem of finding the family of all so called the locally reducible factors in the binary de Bruijn graph of order k is equivalent to the problem of finding all colourings of edges in the binary de Bruijn graph of order k-1, where each vertex belongs to exactly two cycles of different colours. In this paper we define and study such colouring for the greater class of the de Bruijn graphs in order to define a class of so called regular factors, which is not so difficult to construct....

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...

From Bi-ideals to Periodicity

Jānis Buls, Aivars Lorencs (2008)

RAIRO - Theoretical Informatics and Applications

The necessary and sufficient conditions are extracted for periodicity of bi-ideals. They cover infinitely and finitely generated bi-ideals.

GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation

Huijuan WANG, Qiaoyan WEN, Jie ZHANG (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The Legendre symbol has been used to construct sequences with ideal cross-correlation, but it was never used in the arithmetic cross-correlation. In this paper, a new class of generalized Legendre sequences are described and analyzed with respect to their period, distributional, arithmetic cross-correlation and distinctness properties. This analysis gives a new approach to study the connection between the Legendre symbol and the arithmetic cross-correlation. In the end of this paper, possible application...

Linear spans of optimal sets of frequency hopping sequences∗

Gao Juntao, Hu Yupu, Li Xuelian (2012)

RAIRO - Theoretical Informatics and Applications

Frequency hopping sequences sets are required in frequency hopping code division multiple access systems. For the anti-jamming purpose, frequency hopping sequences are required to have a large linear span. In this paper, by using a permutation polynomial δ(x) over a finite field, we transform several optimal sets of frequency hopping sequences with small linear span into ones with large linear span. The exact values of the linear span are presented by using the methods of counting the terms of the...

Linear spans of optimal sets of frequency hopping sequences

Gao Juntao, Hu Yupu, Li Xuelian (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Frequency hopping sequences sets are required in frequency hopping code division multiple access systems. For the anti-jamming purpose, frequency hopping sequences are required to have a large linear span. In this paper, by using a permutation polynomial δ(x) over a finite field, we transform several optimal sets of frequency hopping sequences with small linear span into ones with large linear span. The exact values of the linear span are presented by using the methods of counting the terms of the...

On the joint 2-adic complexity of binary multisequences

Lu Zhao, Qiao-Yan Wen (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with pn-period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the number of multisequences with given joint 2-adic complexity.

On the joint 2-adic complexity of binary multisequences∗

Lu Zhao, Qiao-Yan Wen (2012)

RAIRO - Theoretical Informatics and Applications

Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with pn-period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the number of multisequences...

Sobre el parámetro complejidad lineal y los filtros no lineales de segundo orden.

Amparo Fúster Sabater, Luis J. García Villalba (2000)

Revista Matemática Complutense

A new method of analysing the linear complexity of 2nd-order nonlinear filterings of m-sequences that is based on the concept of regular coset is present. The procedure considers any value of the LFSR's length, L, (prime or composite number). Emphasis is on the geometric interpretation of the regular cosets which produce degeneracies in the linear complexity of the filtered sequence. Numerical expressions to compute the linear complexity of such sequences are given as well as practical rules to...

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