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Workshop on Algebraic Coding

Algebraic Coding 1991: Algebraic Coding pp 75–81Cite as

Saddle point techniques in asymptotic coding theory

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 573))

Abstract

We use asymptotic estimates on coefficients of generating functions to derive anew the asymptotic behaviour of the volume of Hamming spheres and Lee spheres for small alphabets. We then derive the asymptotic volume of Lee spheres for large alphabets, and an asymptotic relation between the covering radius and the dual distance of binary codes.

This work was partially performed while this author was visiting Brown University, Providence, R.I., U.S.A. The author also acknowledges the support of the PRC Mathématique-Informatique (CNRS) and of ESPRIT-II Basic Research Action No. 3075 (project ALCOM).

This work was partially supported by the PRC C3 (CNRS and MRT).

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Author information

Authors and Affiliations

  1. L.R.I., CNRS-URA 410, Université Paris XI, Bât. 490, 91405, Orsay, France

    Danièle Gardy

  2. Laboratoire I.3.S. CNRS-URA 1376, Bât. 4, 250 rue Albert Einstein, Sophia-Antipolis, 06560, Valbonne, France

    Patrick Solé

Authors
  1. Danièle Gardy
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  2. Patrick Solé
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Editor information

Gérard Cohen Antoine Lobstein Gilles Zémor Simon Litsyn

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© 1992 Springer-Verlag Berlin Heidelberg

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Gardy, D., Solé, P. (1992). Saddle point techniques in asymptotic coding theory. In: Cohen, G., Lobstein, A., Zémor, G., Litsyn, S. (eds) Algebraic Coding. Algebraic Coding 1991. Lecture Notes in Computer Science, vol 573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034343

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  • DOI: https://doi.org/10.1007/BFb0034343

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55130-0

  • Online ISBN: 978-3-540-46739-7

  • eBook Packages: Springer Book Archive

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