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Some decoding applications of minimal realization

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Cryptography and Coding (Cryptography and Coding 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1025))

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Abstract

We show that minimal realization (MR) of a finite sequence and the associated MR algorithm [10] provide new solutions to a number of decoding problems: BCH and Reed-Solomon codes, errors and erasures, classical Goppa codes and negacyclic codes. We concentrate on the MR of the DFT of an error polynomial, thus avoiding the “key equation” and Forney's procedure. We also discuss simplification of the theory in characteristic two and an extension of the MR theory to several sequences, obtaining a new simultaneous MR algorithm.

Research supported by U.K. Science and Engineering Research Grant GR/H15141.

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Authors and Affiliations

  1. Centre for Communications Research, University of Bristol, England

    Graham Norton

Authors
  1. Graham Norton
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Colin Boyd

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© 1995 Springer-Verlag Berlin Heidelberg

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Norton, G. (1995). Some decoding applications of minimal realization. In: Boyd, C. (eds) Cryptography and Coding. Cryptography and Coding 1995. Lecture Notes in Computer Science, vol 1025. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60693-9_8

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  • DOI: https://doi.org/10.1007/3-540-60693-9_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60693-2

  • Online ISBN: 978-3-540-49280-1

  • eBook Packages: Springer Book Archive

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