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Algebraic Coding 1993: Algebraic Coding pp 304-315 | Cite as

Product codes and the singleton bound

  • Nicolas Sendrier
Bounds for Codes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 781)

Abstract

Minimum distance is not always the most determinant factor to acheive high performance for error correction. Of course the knowledge of the whole weight distribution of the code is more accurate than the knowledge of the mere minimum distance, and the phenomenon amplifies for a high noise level. Besides this fact, the use of error-correcting codes in practical situations requires a trade-off between the algorithmic complexity and the performance of the decoding procedure. We show here that for low rates a very good trade-off is possible using product codes, although they are known for their poor minimum distance.

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References

  1. [1]
    P. Elias. Error-free coding. IEEE Transaction on Information Theory, 4:29–37, 1954.Google Scholar
  2. [2]
    S.M. Reddy and J.P. Robinson. Random error and burst correction by iterated codes. IEEE Transaction on Information Theory, 18(1):182–185, January 1972.Google Scholar
  3. [3]
    N. Sendrier. Product of linear codes. Rapport de Recherche 1286, INRIA, October 1990.Google Scholar
  4. [4]
    N. Sendrier. Codes Correcteurs d'Erreurs à Haut Pouvoir de Correction. Thèse de doctorat, Université Paris 6, December 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Nicolas Sendrier
    • 1
  1. 1.Domaine de Voluceau, RocquencourtINRIALe Chesnay CedexFrance

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