Abstract.
In an earlier work Hubert and the authors of this paper introduced and studied the notion of pseudorandomness of binary lattices. Later in another paper the authors gave a construction for a large family of “good” binary lattices by using the quadratic characters of finite fields. Here, a further large family of “good” binary lattices is constructed by using finite fields and the notion of multiplicative inverse.
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Á Andics (2005) ArticleTitleOn the linear complexity of binary sequences Ann Univ Sci Budapest Eötvös 48 173–180 Occurrence Handle1121.11050 Occurrence Handle2323628
H Davenport DJ Lewis (1963) ArticleTitleCharacter sums and primitive roots in finite fields Rend Circ Mat Palermo 12 IssueID2 129–136 Occurrence Handle0119.04302 Occurrence Handle167482 Occurrence Handle10.1007/BF02843959
J Eichenauer-Herrmann H Niederreiter (1994) ArticleTitleBounds for exponential sums and their applications to pseudorandom numbers Acta Arith 67 269–281 Occurrence Handle0957.11050 Occurrence Handle1292739
P Hubert C Mauduit A Sárközy (2006) ArticleTitleOn pseudorandom binary lattices Acta Arith 125 51–62 Occurrence Handle1155.11044 Occurrence Handle2275217
DG Kodila (2005) ArticleTitleTime-analysis of pseudorandom bit generators Ann Univ Sci Budapest Eötvös 48 31–43 Occurrence Handle1121.94017 Occurrence Handle2323618
H Liu (2007) ArticleTitleNew pseudorandom sequences constructed by multiplicative inverses Acta Arith 125 11–19 Occurrence Handle10.4064/aa125-1-2
C Mauduit A Sárközy (1997) ArticleTitleOn finite pseudorandom binary sequences, I. Measure of pseudorandomness, the Legendre symbol Acta Arith 82 365–377 Occurrence Handle0886.11048 Occurrence Handle1483689
C Mauduit A Sárközy (2005) ArticleTitleConstruction of pseudorandom binary sequences by using the multiplicative inverse Acta Math Hungar 108 239–252 Occurrence Handle1102.11038 Occurrence Handle10.1007/s10474-005-0222-y Occurrence Handle2162562
C Mauduit A Sárközy (2007) ArticleTitleA On large families of pseudorandom binary lattices Uniform distribution theory 2 23–37 Occurrence Handle2318530 Occurrence Handle05247160
H Niederreiter JE Shparlinski (2000) ArticleTitleExponential sums and the distribution of inverse congruential pseudorandom numbers with prime-power modulus Acta Arith 92 89–98 Occurrence Handle0949.11036 Occurrence Handle1739735
H Niederreiter A Winterhof (2005) ArticleTitleExponential sums and the distribution of inversive congruential pseudorandom numbers with power of two modulus Int J Number Theory 1 431–438 Occurrence Handle1084.11042 Occurrence Handle10.1142/S1793042105000261 Occurrence Handle2175100
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Authors’ addresses: Christian Mauduit, Institut de Mathématiques de Luminy, CNRS, UMR 6206, 163 avenue de Luminy, Case 907, F-13288 Marseille Cedex 9, France; András Sárközy, Department of Algebra and Number Theory, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
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Mauduit, C., Sárközy, A. Construction of pseudorandom binary lattices by using the multiplicative inverse. Monatsh Math 153, 217–231 (2008). https://doi.org/10.1007/s00605-007-0479-z
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DOI: https://doi.org/10.1007/s00605-007-0479-z