The Lattice HKO44

An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de) and
Neil J. A. Sloane, AT&T Shannon Labs (njas@research.att.com)

Last modified Sat Jun 23 22:43:14 EDT 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
BASIS (multiplied by sqrt(6))
MINIMAL_NORM
PROPERTIES
KISSING_NUMBER
COMMENTS
LAST_LINE

• NAME
  HKO44
  
• DIMENSION
  44
  
• DET
  1
  
• BASIS (multiplied by sqrt(6))
  44 44
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 3 1 1 0 1 3 1 3 3 3 3 3 3 3 1 5 3 3 3 3 5
  0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 2 1 5 1 4 4 2 0 4 0 4 4 4 0 2 0 0 4 4 4
  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 3 5 2 1 2 4 2 2 4 0 4 2 0 4 2 2 0 2 4
  0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 1 3 0 2 3 0 2 2 0 0 4 0 4 4 2 4 4 4 2
  0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 1 2 4 0 1 4 0 2 4 2 0 2 2 0 4 4 0 0
  0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 4 5 1 4 2 4 0 1 4 4 4 4 2 0 4 2 2 0 0 0
  0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 4 1 5 2 0 2 2 2 3 0 4 2 2 4 2 0 2 2 4 0
  0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 1 0 0 0 2 4 2 1 0 0 4 0 0 4 0 2 4 0
  0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 3 5 4 0 4 4 0 2 0 3 4 4 4 0 4 4 2 2 4
  0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 1 2 2 2 2 4 4 4 4 3 2 4 0 4 0 0 0 4
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 4 2 4 3 3 0 2 4 2 2 2 2 2 0 3 0 4 4 4 2 0 0
  0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 5 1 3 4 3 3 1 3 3 1 3 3 5 5 5 1 3 5 3 5 3 3
  0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 3 0 4 4 2 0 2 4 4 4 4 0 2 4 4 4 4 3
  0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 5 1 4 4 0 4 2 2 0 0 0 4 4 2 2 0 2 3 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2 2 4 5 1 4 0 2 4 2 0 0 4 4 2 1 4 4 2 0 0 4
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 4 2 3 3 0 0 0 2 4 4 2 4 4 0 4 5 2 0 0 2 2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 5 5 4 4 4 4 4 4 4 0 4 0 0 2 3 4 2 4 4
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 4 4 4 2 4 2 2 0 4 0 2 2 3 2 4 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 5 3 2 0 0 4 0 4 4 0 4 4 0 4 2 4 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 4 5 1 2 0 4 2 2 4 2 4 2 0 0 0 2 2 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 5 5 1 4 2 0 0 2 4 2 4 0 0 0 2 4 2 0 2 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 2 4 5 3 0 4 4 4 2 4 2 4 0 2 4 4 4 4 4 0 4
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
  
• MINIMAL_NORM
  4
  
• PROPERTIES
  UNIMODULAR = 1
  
• KISSING_NUMBER
  8008
  
• COMMENTS
  Sent by Michio Ozeki (ozeki@kszaoh3.kj.yamagata-u.ac.jp), May 30, 2001.
  "Here I report some of the results of joint work by me, Harada and
  Kitazume (in Chiba Univ.) under preparation.
  We extend the method given in my ternary code
  construction paper in 1989 to Z_6 codes.
  We get the known 48-dimensional lattices
  P_{48,p},P_{48,q}, an explicit basis for
  a 56-dimensioal extremal type II lattice,
  an explicit 64-dimensional extremal type II lattice,
  an explicit basis of 44-dimensional odd unimodular
  lattice with minimal norm 4, and an explicit basis
  for a 60-dimensional odd unimodular lattice with minimal
  norm 6."
  
• LAST_LINE
  
  

INDEX FILE | ABBREVIATIONS

[ AT&T Labs Research | Our People | Our Work | History | Find ]