Skip to main content
SpringerLink
Log in

Substitution of characters in q-ary m-sequences

  • Submitted Contributions
  • Conference paper
  • First Online:
Book cover Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 508))

Abstract

This paper discusses a simple way of increasing the linear complexity of maximal length q-ary sequences. This is attained by using character substitution tables. The achievable maximum of increase is determined and it is shown that a portion of about 1/e of all substitution tables share this maximum. The mean value and the variance of the linear complexity is derived for the sequence's output by randomly chosen substitutions. The special case of permutations as substitutions are investigated, as well. At the end of the paper we propose an extension of the notion of linear complexity.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zierler, N., "Linear recurring sequences", J.SIAM, Vol.7, 1959.

    Google Scholar 

  2. Golomb, S. W., Shift-Register Sequences. San Francisco: Holden Day, 1967.

    Google Scholar 

  3. Massey, J.L., "Shift-Register Synthesis and BCH Decoding", IEEE Trans. Inform. Theory, Vol. IT-15, Jan. 1969. 4.

    Google Scholar 

  4. Key, E.L., "An analysis of the structure and complexity of nonlinear binary sequence generators", IEEE Trans. Inform. Theory, IT-22, No. 6., Nov. 1976.

    Google Scholar 

  5. L. Brynielson, "On the Linear Complexity of Combined Shift Register Sequences", Advances in Cryptology — Eurocrypt '85, Lecture Notes in Computer Science, No. 219, Springer, 1985.

    Google Scholar 

  6. Simon, M.K., Omura, J.K., Scholtz, R.A., Levitt, B.K., Spread Spectrum Communications, Vol 1., Ch.5., Computer Science Press, 1985.

    Google Scholar 

  7. Rueppel, R.A., New Approaches to Stream Ciphers. Communication and Control Series of Engineering, Springer Verlag, 1986.

    Google Scholar 

  8. T. Siegenthaler, Methoden für den Entwurf von Stream Cipher-Systemen, Doctoral Thesis, ETH Zürich, 1986

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technical University of Budapest, Stoczek u.2., H-1111, Budapest

    István Vajda

  2. Math. Inst. of the HAS, Realtanoda u. 13-15, H-1053, Budapest

    Tibor Nemetz

Authors
  1. István Vajda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tibor Nemetz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Shojiro Sakata

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vajda, I., Nemetz, T. (1991). Substitution of characters in q-ary m-sequences. In: Sakata, S. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1990. Lecture Notes in Computer Science, vol 508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54195-0_42

Download citation

  • DOI: https://doi.org/10.1007/3-540-54195-0_42

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54195-0

  • Online ISBN: 978-3-540-47489-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation