New pseudorandom sequences constructed by quadratic residues and Lehmer numbers

Liu, Huaning

doi:10.1090/s0002-9939-06-08630-8

Cited by 11 publications

(12 citation statements)

References 14 publications

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“…Later many pseudorandom binary sequences were given and studied (see [3], [4], [6], [7], [8], [9], [11], [12], [13], [15], [16], [19], and [23]). For example, let p be an odd prime, e (1) n = n p , and E…”

Section: Introduction and Resultsmentioning

confidence: 99%

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A large family of pseudorandom binary lattices

Liu

2008

Proc. Amer. Math. Soc.

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Abstract. Recently P. Hubert, C. Mauduit and A. Sárközy introduced and studied the notion of pseudorandomness of binary lattices and gave a pseudorandom binary lattice. Later in other papers C. Mauduit and A. Sárközy constructed some large families of "good" binary lattices. In this paper a large family of pseudorandom binary lattices is presented by using the multiplicative inverse and the quadratic character of finite fields.

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Section: Introduction and Resultsmentioning

confidence: 99%

“…The author [12] studied the pseudorandomness of E (2) p−1 . Moreover, let f (x), g(x) ∈ F p [x], and …”

Section: Introduction and Resultsmentioning

confidence: 99%

A large family of pseudorandom binary lattices

Liu

2008

Proc. Amer. Math. Soc.

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“…Since that many constructions have been given for binary sequences with strong pseudorandom properties (see, e.g., [10], [11], [16], [17], [29], [30], [31], [36], [37], [39]). …”

Section: Introductionmentioning

confidence: 99%

The cross-correlation measure for families of binary sequences

Gyarmati¹,

Mauduit²,

Sárközy³

2014

Applied Algebra and Number Theory

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Large families of binary sequences of the same length are considered and a new measure, the cross-correlation measure of order k is introduced to study the connection between the sequences belonging to the family. It is shown that this new measure is related to certain other important properties of families of binary sequences. Then the size of the cross-correlation measure is studied. Finally, the cross-correlation measures of two important families of pseudorandom binary sequences are estimated.

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“…Later several constructions have been proposed which have good pseudorandom properties in terms of these measures: for example, the Legendre symbol sequence [4], [11]; sequences generated by the multiplicative inverse [12] and its extensions [7], [15]; the sequences generated by using elliptic curves [1], [2], [9], [16]. See also the survey paper [18].…”

Section: Introductionmentioning

confidence: 99%