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A correction to: on the linear complexity of the Sidelnikov–Lempel–Cohn–Eastman sequences

  • Minglong QiEmail author
  • Shengwu Xiong
Commentary
  • 9 Downloads

Abstract

In the paper of Kyureghyan and Pott (Des Codes Cryptogr 29:149–164, 2003), the linear feedback polynomials of the Sidelnikov–Lempel–Cohn–Eastman sequences were determined for some special cases. We found that Corollary 4 and Theorem 2 of that paper are wrong because there exist counterexamples for these two results. In this note, we give some counterexamples of Corollary 4 and Theorem 2, and correct them by readopting the negation of the condition of Lemma 5 as their necessary and sufficient conditions.

Keywords

Linear feedback polynomial Linear complexity The Sidelnikov–Lempel–Cohn–Eastman sequences Jacobsthal sums 

Mathematics Subject Classification

94A55 

Notes

Acknowledgements

The authors of the present corrigendum thank very much the anonymous reviewer and the editor for their valuable comments and analysis. Minglong Qi was supported by the Foundation for the project Middleware Technologies of the Wuhan University of Technology under Grant 2012037. Shengwu Xiong was supported by the Foundation for the project Formation Model for Engineers in Software Engineering of Hubei Province under Grant 2012103.

References

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    Berndt B.C., Evans R.J., Williams K.S.: Gauss and Jacobi Sums. Wiley, New York (1998).zbMATHGoogle Scholar
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    Kyureghyan G.M., Pott A.: On the linear complexity of the Sidelnikov–Lempel–Cohn–Eastman sequences. Des. Codes Cryptogr. 29, 149–164 (2003).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Lidl R., Niederreiter H.: Finite Fields, Encyclopedia of Mathematics and Its Applications, vol. 20, 2nd edn. Cambridge University Press, Cambridge (1997).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyWuhan University of TechnologyWuhanChina

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