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)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

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

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