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Encounters with the Berlekamp-Massey Algorithm

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Book cover Communications and Cryptography

Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 276))

Abstract

In 1969, J. Massey published a now-famous paper showing, among other things, that an iterative algorithm introduced by Berlekamp for decoding BCH codes also solved the problem of finding a shortest-length feedback shift register circuit for generating a given finite sequence of digits. This nice physical interpretation opened the door to connections with many other problems, including the minimal partial realization problems of linear system theory, Padé approximations and continued fractions, the fast algorithms of Levinson and Schur for Toeplitz matrices, inverse scattering, VLSI implementations, etc. This paper is an informal account of some of the different contexts in which the Berlekamp-Massey algorithm have been encountered in the work of the author and his students.

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*This work was supported in part by the Army Research Office under Grant DAAH04-93-G-0029.

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Author information

Authors and Affiliations

  1. Dept. of Electrical Engineering, Stanford University, Stanford, CA, 94305-4055, USA

    Thomas Kailath

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  1. Thomas Kailath
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Editor information

Editors and Affiliations

  1. University of Illinois, USA

    Richard E. Blahut

  2. University of Notre Dame, France

    Daniel J. Costello Jr.

  3. ETH Zurich, Switzerland

    Ueli Maurer

  4. University of California, San Diego, USA

    Thomas Mittelholzer

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© 1994 Springer Science+Business Media New York

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Kailath, T. (1994). Encounters with the Berlekamp-Massey Algorithm. In: Blahut, R.E., Costello, D.J., Maurer, U., Mittelholzer, T. (eds) Communications and Cryptography. The Springer International Series in Engineering and Computer Science, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2694-0_21

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  • DOI: https://doi.org/10.1007/978-1-4615-2694-0_21

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6159-6

  • Online ISBN: 978-1-4615-2694-0

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