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A Gröbner basis and a minimal polynomial set of a finite nD array

  • Shojiro Sakata
Submitted Contributions Bases
Part of the Lecture Notes in Computer Science book series (LNCS, volume 508)

Abstract

In this paper, the relationship between a Gröbner basis and a minimal polynomial set of a finite nD array is discussed. A minimal polynomial set of a finite nD array is determined by the nD Berlekamp-Massey algorithm. It is shown that a minimal polynomial set is not always a Gröbner basis even if the uniqueness condition is satisfied, and a stronger sufficient condition for a minimal polynomial set to be a Gröbner basis is presented. Furthermore, a simple test whether a given set of polynomials is a Gröbner basis is proposed based on the theory of nD linear recurring arrays. The observations will be important in applying the nD Berlekamp-Massey algorithm to decode some kinds of nD cyclic codes and algebraic geometry codes.

Keywords

Uniqueness Condition Characteristic Polynomial Total Order Cyclic Code Infinite Array 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Shojiro Sakata
    • 1
  1. 1.Department of Knowledge-Based Information EngineeringToyohashi University of TechnologyToyohashiJapan

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