Double Circulant Codes over Z_4 and Even Unimodular Lattices

A. R. Calderbank(*) and N. J. A. Sloane(*)

Mathematical Sciences Research Center 
AT&T Bell Laboratories 
Murray Hill, New Jersey 07974 

July 16, 1996 


ABSTRACT

With the help of some new results about weight enumerators of self-dual
codes over Z_4 we investigate a class of double circulant codes
over Z_4, one of which leads to an extremal even unimodular
40-dimensional lattice. It is conjectured that there should be
"Nine more constructions of the Leech lattice".
[These have since been found.]


For the full version see
http://www.research.att.com/~njas/doc/mckay.pdf (pdf) or
http://www.research.att.com/~njas/doc/mckay.ps (ps)


(*) Present address:
Information Sciences Research
AT&T Shannon Lab
Florham Park, NJ 07932-0971 USA
Email: njas@research.att.com

This paper was published (in a somewhat different form) in
J. Algebraic Combinatorics, 6 (1997), 119-131.