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Synthesis of two-dimensional linear feedback shift registers and Groebner bases

  • Shojiro Sakata
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 356)

Abstract

In this paper we discuss about how to design a two-dimensional linear feedback shift register. It is a switching circuit capable of generating a prescribed doubly periodic array. In particular, it can be used as an encoder of a two-dimensional cyclic code. Our method is based on a two-dimensional extension of the Berlekamp-Massey algorithm for synthesis of a (one-dimensional) linear feedback shift register. In the sequel, we make clear that our problem is equivalent to constructing a Groebner basis of the ideal which is defined by the given array.

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References

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    Imai H., A theory of two-dimensional cyclic codes, Information and Control, vol. 34, pp.1–21, 1979.CrossRefGoogle Scholar
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    Berlekamp E.R., Nonbinary BCH decoding,’ Algebraic Coding Theory', Chapters 7 and 10, 1968.Google Scholar
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    Massey J.L., Shift-register synthesis and BCH decoding, IEEE Trans. Information Theory, vol. IT-15, pp.122–127, 1969.CrossRefGoogle Scholar
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    Sakata S., General theory of doubly periodic arrays over an arbitrary finite field and its applications, IEEE Trans. Information Theory, vol. IT-24, pp.719–730, 1978.CrossRefGoogle Scholar
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    Sakata S., Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array, J. of Symbolic Computation, vol. 5, pp.321–337, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Shojiro Sakata
    • 1
  1. 1.Toyohashi University of TechnologyToyohashiJapan

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