Minimum-autocorrelation sequences
C. Zaremba (1963)
Applicationes Mathematicae
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C. Zaremba (1963)
Applicationes Mathematicae
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Mercer, A.McD. (1978)
International Journal of Mathematics and Mathematical Sciences
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(2012)
Acta Arithmetica
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Hiroyuki Okazaki (2015)
Formalized Mathematics
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In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation...
David J. S. Mayor, Harald Niederreiter (2007)
Acta Arithmetica
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Jovan D. Kečkić (1973)
Publications de l'Institut Mathématique
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Hans Carstens (1975)
Fundamenta Mathematicae
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Binod Chandra Tripathy, Bipul Sarma (2007)
Mathematica Slovaca
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D. F. Dawson (1969)
Matematički Vesnik
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Henri Faure, Christiane Lemieux (2016)
Acta Arithmetica
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Sobol' sequences are a popular family of low-discrepancy sequences, in spite of requiring primitive polynomials instead of irreducible ones in later constructions by Niederreiter and Tezuka. We introduce a generalization of Sobol' sequences that removes this shortcoming and that we believe has the potential of becoming useful for practical applications. Indeed, these sequences preserve two important properties of the original construction proposed by Sobol': their generating matrices...