Double Circulant Codes over Z\!Z_{\bf 4}and Even Unimodular Lattices

  • Authors:
  • A. R. Calderbank;N. J. A. Sloane

  • Affiliations:
  • Information Sciences Research Center, AT&/T Labs-Research, Murray Hill, New Jersey 07974/ E-mail: rc@research.att.com, njas@research.att.com;Information Sciences Research Center, AT&/T Labs-Research, Murray Hill, New Jersey 07974/ E-mail: rc@research.att.com, njas@research.att.com

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 1997

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Abstract

With the help of some new results about weight enumeratorsof self-dual codes over Z\!Z_4 we investigate a class of doublecirculant codes over Z\!Z_4, one of which leads to anextremal even unimodular 40-dimensional lattice. It is conjecturedthat there should be “Nine more constructions of the Leech lattice”