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Construction of large families of pseudorandom binary sequences

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Abstract

Oon constructed large families of finite binary sequences with strong pseudorandom properties by using Dirichlet characters of large order. In this paper Oon’s construction is generalized and extended. We prove that in our construction the well-distribution and correlation measures are as “small” as in the case of the Legendre symbol.

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References

  1. Ahlswede, R., Mauduit, C., Sárközy, A.: Large families of pseudorandom sequences of k symbols and their complexity, Part I and II. In: General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol. 4123, pp. 293–325. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  2. Davenport, H.: Multiplicative Number Theory, 2nd edn. Springer, New York (1980)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  4. Gyarmati, K.: A note to the earlier paper: On a fast version of a pseudorandom generator. Ann. Univ. Sci. Budapest Eötvös 49, 87–93 (2006)

    MATH  MathSciNet  Google Scholar 

  5. Gyarmati, K.: On a fast version of a pseudorandom generator. In: General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol. 4123, pp. 326–342. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  9. Oon, S.M.: Construction des suites binaires pseudo-aléatories. PhD thesis, Nancy (2005)

  10. Oon, S.M.: On pseudo-random properties of certain Dirichlet series. Ramanujan J. 15, 19–30 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Schmidt, W.M.: Equations over Finite Fields. An Elementary Approach. Lecture Notes in Math., vol. 536. Springer, New York (1976)

    MATH  Google Scholar 

  12. Vinogradov, I.M.: Elements of Number Theory. Dover Publications, New York (1954)

    MATH  Google Scholar 

  13. Weil, A.: Sur les Courbes Algébriques et les Variétés qui s’en Déduisent. In: Act. Sci. Ind., vol. 1041. Hermann, Paris (1948)

    Google Scholar 

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Authors and Affiliations

  1. Eötvös Loránd University, Pazmany Peter setany 1/c, Budapest, 1117, Hungary

    László Mérai

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  1. László Mérai
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Mérai, L. Construction of large families of pseudorandom binary sequences. Ramanujan J 18, 341–349 (2009). https://doi.org/10.1007/s11139-008-9131-3

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  • DOI: https://doi.org/10.1007/s11139-008-9131-3

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