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A note on certain modular constructions of pseudorandom binary sequences with composite moduli

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Abstract

J. Rivat and A. Sárközy extended two large families of pseudorandom binary sequences to the case of composite moduli m, where m is the product of two different primes not far apart. In this paper we continue the study in this direction. We shall improve the estimates for the correlation measure of the sequences.

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References

  1. J. Cassaigne, S. Ferenczi, C. Mauduit, J. Rivat and A. Sárközy, On finite pseudorandom binary sequences III: the Liouville function I, Acta Arith., 87 (1999), 367–390.

    MathSciNet  MATH  Google Scholar 

  2. L. Goubin, C. Mauduit and A. Sárközy, Construction of large families of pseudorandom binary sequences, J. Number Theory, 106 (2004), 56–69.

    Article  MathSciNet  MATH  Google Scholar 

  3. K. Gyarmati, On a family of pseudorandom binary sequences, Period. Math. Hungar., 49 (2004), 45–63.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Hubert, C. Mauduit and A. Sárközy, On pseudorandom binary lattices, Acta Arith., 125 (2006), 51–62.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Liu, New pseudorandom sequences constructed by quadratic residues and Lehmer numbers, Proc. Amer. Math. Soc., 135 (2007), 1309–1318.

    Article  MathSciNet  MATH  Google Scholar 

  6. H. Liu, A family of pseudorandom binary sequences constructed by the multiplicative inverse, Acta Arith., 130 (2007), 167–180.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Liu, T. Zhan and X. Wang, On the correlation of pseudorandom binary sequences with composite moduli, Publ. Math. Debrecen, 74 (2009), 195–214.

    MathSciNet  MATH  Google Scholar 

  8. C. Mauduit, J. Rivat and A. Sárközy, Construction of pseudorandom binary sequences using additive characters, Monatsh. Math., 141 (2004), 197–208.

    Article  MathSciNet  MATH  Google Scholar 

  9. C. Mauduit and A. Sárközy, On finite pseudorandom binary sequences I: measure of pseudorandomness, the Legendre symbol, Acta Arith., 82 (1997), 365–377.

    MathSciNet  MATH  Google Scholar 

  10. C. Mauduit and A. Sárközy, Construction of pseudorandom binary sequences by using the multiplicative inverse, Acta Math. Hungar., 108 (2005), 239–252.

    Article  MathSciNet  MATH  Google Scholar 

  11. C. Mauduit and A. Sárközy, On large families of pseudorandom binary lattices, Unif. Distrib. Theory, 2 (2007), 23–37.

    MathSciNet  MATH  Google Scholar 

  12. J. Rivat and A. Sárközy, Modular constructions of pseudorandom binary sequences with composite moduli, Period. Math. Hungar., 51 (2005), 75–107.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Schmidt, Equations Over Finite Fields: An Elementary Approach, Lecture Notes in Mathematics 536, Springer, Berlin, 1976.

    MATH  Google Scholar 

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Correspondence to Huaning Liu.

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Communicated by András Sárközy

Supported by the National Natural Science Foundation of China under Grant No. 10901128, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20090201120061, the Natural Science Foundation of the Education Department of Shaanxi Province of China under Grant No. 09JK762, and the Fundamental Research Funds for the Central University.

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Liu, H., Gao, J. A note on certain modular constructions of pseudorandom binary sequences with composite moduli. Period Math Hung 67, 175–185 (2013). https://doi.org/10.1007/s10998-013-8920-7

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  • DOI: https://doi.org/10.1007/s10998-013-8920-7

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