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Algebraic Coding 1993: Algebraic Coding pp 194-205 | Cite as

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

  • Alexis Bonnecaze
  • Patrick Solé
Sphere Packings and Lattices
Part of the Lecture Notes in Computer Science book series (LNCS, volume 781)

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.

Key words

Codes Weight Enumerators Self-Dual Quaternary Codes Formally Self-Dual Binary Codes Unimodular Lattices 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Alexis Bonnecaze
    • 1
  • Patrick Solé
    • 1
  1. 1.CNRSValbonneFrance

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