Skip to main content
Top
Published in: Applicable Algebra in Engineering, Communication and Computing 4/2014

01-08-2014 | Original Paper

On pseudorandom sequences of \(k\) symbols constructed using finite fields

Authors: Xiaoni Du, Zhixing Lin

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 4/2014

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A family of pseudorandom sequences of \(k\) symbols are constructed by using finite fields of prime-power order. The construction is an extension of certain construction of Sárközy and Winterhof on binary sequences using the quadratic character with polynomial arguments over any finite fields, and of certain construction of Ahlswede, Mauduit and Sárközy on sequences of \(k\) symbols using multiplicative characters with polynomial arguments over finite prime fields. Certain pseudorandom measures of the resulting sequences are considered.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Ahlswede R., Mauduit C., Sárközy A.: Large families of pseudorandom sequences of \(k\) symbols and their complexity, Part I. In: General Theory of Information Transfer and Combinatorics, LNCS, vol. 4123, pp. 293–307. Springer, Berlin (2006) Ahlswede R., Mauduit C., Sárközy A.: Large families of pseudorandom sequences of \(k\) symbols and their complexity, Part I. In: General Theory of Information Transfer and Combinatorics, LNCS, vol. 4123, pp. 293–307. Springer, Berlin (2006)
2.
go back to reference Ahlswede R., Mauduit C., Sárközy A.: Large families of pseudorandom sequences of \(k\) symbols and their complexity, Part II. In: General Theory of Information Transfer and Combinatorics, LNCS, vol. 4123, pp. 308–325. Springer, Berlin (2006) Ahlswede R., Mauduit C., Sárközy A.: Large families of pseudorandom sequences of \(k\) symbols and their complexity, Part II. In: General Theory of Information Transfer and Combinatorics, LNCS, vol. 4123, pp. 308–325. Springer, Berlin (2006)
3.
go back to reference Bérczi, G.: On finite pseudorandom sequences of \(k\) symbols. Period. Math. Hung. 47(1–2), 29–44 (2003)MATH Bérczi, G.: On finite pseudorandom sequences of \(k\) symbols. Period. Math. Hung. 47(1–2), 29–44 (2003)MATH
4.
go back to reference Cassaigne, J., Mauduit, C., Sárközy, A.: On finite pseudorandom binary sequences, VII: the measures of pseudorandomness. Acta Arith. 103, 97–118 (2002)CrossRefMATHMathSciNet Cassaigne, J., Mauduit, C., Sárközy, A.: On finite pseudorandom binary sequences, VII: the measures of pseudorandomness. Acta Arith. 103, 97–118 (2002)CrossRefMATHMathSciNet
5.
go back to reference Chen, Z., Winterhof, A.: Linear complexity profile of m-ary pseudorandom sequences with small correlation measure. Indag. Math. 20(4), 631–640 (2009)CrossRefMATHMathSciNet Chen, Z., Winterhof, A.: Linear complexity profile of m-ary pseudorandom sequences with small correlation measure. Indag. Math. 20(4), 631–640 (2009)CrossRefMATHMathSciNet
6.
go back to reference Chen, Z., Gomez, D., Winterhof, A.: Distribution of digital explicit inversive pseudorandom numbers and their binary threshold sequence. In: L’Ecuyer, Pierre, Owen, Art B. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2008, pp. 249–258. Springer, Heidelberg (2009)CrossRef Chen, Z., Gomez, D., Winterhof, A.: Distribution of digital explicit inversive pseudorandom numbers and their binary threshold sequence. In: L’Ecuyer, Pierre, Owen, Art B. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2008, pp. 249–258. Springer, Heidelberg (2009)CrossRef
7.
go back to reference Goubin, L., Mauduit, C., Sárközy, A.: Construction of large families of pseudorandom binary sequences. J. Number Theory 106(1), 56–694 (2004)CrossRefMATHMathSciNet Goubin, L., Mauduit, C., Sárközy, A.: Construction of large families of pseudorandom binary sequences. J. Number Theory 106(1), 56–694 (2004)CrossRefMATHMathSciNet
9.
go back to reference Mauduit, C., Sárközy, A.: On finite pseudorandom binary sequences I: measures of pseudorandomness, the Legendre symbol. Acta Arith. 82, 365–377 (1997)MATHMathSciNet Mauduit, C., Sárközy, A.: On finite pseudorandom binary sequences I: measures of pseudorandomness, the Legendre symbol. Acta Arith. 82, 365–377 (1997)MATHMathSciNet
10.
11.
go back to reference Mauduit, C., Sárközy, A.: On large families of pseudorandom binary lattices. Unif. Distrib. Theory 2(1), 23–37 (2007)MATHMathSciNet Mauduit, C., Sárközy, A.: On large families of pseudorandom binary lattices. Unif. Distrib. Theory 2(1), 23–37 (2007)MATHMathSciNet
12.
go back to reference Meidl, W., Winterhof, A.: On the autocorrelation of cyclotomic generator. In: Fq7 2003, LNCS, vol. 2948, pp. 1–11. Springer, Berlin Heidelberg (2003) Meidl, W., Winterhof, A.: On the autocorrelation of cyclotomic generator. In: Fq7 2003, LNCS, vol. 2948, pp. 1–11. Springer, Berlin Heidelberg (2003)
13.
go back to reference Mérai, L.: On finite pseudorandom lattices of \(k\) symbols. Monatsh. Math. 161(2), 173–191 (2009)CrossRef Mérai, L.: On finite pseudorandom lattices of \(k\) symbols. Monatsh. Math. 161(2), 173–191 (2009)CrossRef
14.
go back to reference Sárközy, A., Winterhof, A.: Measures of pseudorandomness for binary sequences constructed using finite fields. Discret. Math. 309, 1327–1333 (2009)CrossRefMATH Sárközy, A., Winterhof, A.: Measures of pseudorandomness for binary sequences constructed using finite fields. Discret. Math. 309, 1327–1333 (2009)CrossRefMATH
15.
go back to reference Schmidt, W.M.: Equations over Finite Fields. An Elementary Approach, Lecture Notes in Mathematics, vol. 536. Springer, Berlin-New York (1976) Schmidt, W.M.: Equations over Finite Fields. An Elementary Approach, Lecture Notes in Mathematics, vol. 536. Springer, Berlin-New York (1976)
Metadata
Title
On pseudorandom sequences of symbols constructed using finite fields
Authors
Xiaoni Du
Zhixing Lin
Publication date
01-08-2014
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 4/2014
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-014-0224-5

Other articles of this Issue 4/2014

Applicable Algebra in Engineering, Communication and Computing 4/2014 Go to the issue

Premium Partner