The BM Algorithm and the BMS Algorithm

  • Shojiro Sakata
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 485)


We present a brief overview of the Berlekamp-Massey (BM) algorithm and of the Berlekamp-Massey-Sakata (BMS) algorithm, with an emphasis on a close relationship between them, which can be summarized as follows: BM algorithm + Gröbner basis = BMS algorithm. Furthermore, we describe various forms of these algorithms, all of which are related to fast decoding of algebraic codes including algebraic-geometric (AG) codes. As a byproduct, we obtain a recursive BMS algorithm which is an extension of Blahut’s recursive BM algorithm. Throughout this paper, we recall the assertions of R.E. Blahut on the importance of fast decoding for good codes, particularly as described in his books, which have spurred recent developments of novel decoding algorithms of AG codes.


Total Order Polynomial Vector Linear Feedback Shift Register Linear Recurrence Algebraic Code 
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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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Shojiro Sakata
    • 1
  1. 1.Department of Computer Science and MathematicsUniversity of Electro-CommunicationsChofu-ShiJapan

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