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On finite pseudorandom lattices of k symbols

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Abstract

In earlier papers Mauduit and Sárközy have introduced and studied the measures of pseudorandomness for finite binary sequences and sequences of k symbols. Later they (with further coauthors) extended the notation of binary sequences to binary lattices. In this paper measures of pseudorandom lattices of k symbols are introduced and studied for “truly random” lattices.

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References

  1. Alon N., Kohayakawa Y., Mauduit C., Moreira C.G., Rödl V.: Measures of pseudorandomness for finite sequences: typical values. Proc. Lond. Math. Soc. 95(3), 778–812 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bérczi G.: On finite pseudorandom sequences of k symbols. Period. Math. Hungar. 47(1–2), 29–44 (2003)

    MATH  MathSciNet  Google Scholar 

  3. Cassaigne J., Mauduit C., Sárközy A.: On finite pseudorandom binary sequences VII: the measures of pseudorandomness. Acta Arith. 103(2), 97–118 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Davenport H., Lewis D.J.: Character sums and primitive roots in finite fields. Rend. Circ. Mat. Palermo 12(2), 129–136 (1963)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Mauduit C., Sárközy A.: On large families of pseudorandom binary lattices. Unif. Distrib. Theory 2(1), 23–37 (2007)

    MATH  MathSciNet  Google Scholar 

  7. Mauduit C., Sárközy A.: Construction of pseudorandom binary lattices by using the multiplicative inverse. Monatsh. Math. 153(3), 217–231 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. 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 

  9. Mauduit C., Sárközy A.: On finite pseudorandom sequences of k symbols. Indag. Math. (N.S.) 13(1), 89–101 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Sárközy A.: On finite pseudorandom binary sequences and their applications in cryptography. Tatra Mt. Math. Publ 37, 123–136 (2007)

    MATH  MathSciNet  Google Scholar 

  11. Topuzoğ lu, A., Winterhof, A.: Pseudorandom Sequences, Topics in Geometry, Coding Theory and Cryptography. Algebr. Appl., vol. 6, pp. 135–166. Springer, Dordrecht (2007)

  12. Winterhof A.: Some estimates for character sums and applications. Des. Codes Crytogr. 22, 123–131 (2001)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Algebra and Number Theory, Eötvös Loránd University, Pázmány Péter sétány 1/c, 1117, Budapest, Hungary

    László Mérai

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  1. László Mérai
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Correspondence to László Mérai.

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Communicated by J. Schoißengeier.

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Mérai, L. On finite pseudorandom lattices of k symbols. Monatsh Math 161, 173–191 (2010). https://doi.org/10.1007/s00605-009-0174-3

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  • DOI: https://doi.org/10.1007/s00605-009-0174-3

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