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Quaternary constructions of formally self-dual binary codes and unimodular lattices

  • Sphere Packings and Lattices
  • Conference paper
  • First Online:
Algebraic Coding (Algebraic Coding 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 781))

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Abstract

Quaternary codes have been studied recently in connection with the construction of sequences with low correlation, lattices and good non linear codes (Kerdock, Preparata). In this paper, we construct formally self-dual binary codes and unimodular lattices using quaternary codes. Two different processes are studied: constructions using Hensel lifting and (u¦u+v) construction. We give a number of examples of formally self-dual binary codes of length n≤64. We obtain a new construction of the Leech lattice, and two new constructions of the Gosset lattice.

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References

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Authors and Affiliations

  1. CNRS, I3S, 250, rue A. Einstein, 06 560, Valbonne, France

    Alexis Bonnecaze & Patrick Solé

Authors
  1. Alexis Bonnecaze
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  2. Patrick Solé
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Editor information

G. Cohen S. Litsyn A. Lobstein G. Zémor

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© 1994 Springer-Verlag Berlin Heidelberg

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Bonnecaze, A., Solé, P. (1994). Quaternary constructions of formally self-dual binary codes and unimodular lattices. In: Cohen, G., Litsyn, S., Lobstein, A., Zémor, G. (eds) Algebraic Coding. Algebraic Coding 1993. Lecture Notes in Computer Science, vol 781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57843-9_20

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  • DOI: https://doi.org/10.1007/3-540-57843-9_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57843-7

  • Online ISBN: 978-3-540-48357-1

  • eBook Packages: Springer Book Archive

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