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The Ubiquity of Reed-Muller Codes

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2227))

Abstract

It is argued that the nearly fifty-year-old Reed-Muller codes underlie a surprisingly large number of algebraic problems in coding and cryptography. This thesis is supported by examples that include some new results such as the construction of a new class of constant-weight cyclic codes with a remarkably simple decoding algorithm and a much simplified derivation of the well-known upper bound on the linear complexity of the running key produced by a nonlinearly filtered maximallength shift-register.

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Author information

Authors and Affiliations

  1. ETH-Zürich and Lund University, Trondhjemsgade 3 2TH, DK-2100, Copenhagen East

    James L. Massey

Authors
  1. James L. Massey
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Editor information

Editors and Affiliations

  1. Department of Mathematics, RMIT University, GPO Box 2476V, 3001, Melbourne, Australia

    Serdar Boztaş

  2. Department of Computing, Macquarie University, 2109, NSW, Australia

    Igor E. Shparlinski

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© 2001 Springer-Verlag Berlin Heidelberg

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Massey, J.L. (2001). The Ubiquity of Reed-Muller Codes. In: Boztaş, S., Shparlinski, I.E. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2001. Lecture Notes in Computer Science, vol 2227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45624-4_1

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  • DOI: https://doi.org/10.1007/3-540-45624-4_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42911-1

  • Online ISBN: 978-3-540-45624-7

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