Shadow lattices and shadow codes

Discrete Mathematics

Volumn 219, Issue 1-3, 2000, Pages 49-64

  Dougherty, Steven T ^a   Harada, Masaaki ^b   Solé, Patrick ^c  

^a UNIVERSITY OF SCRANTON   (United States)

^b YAMAGATA UNIVERSITY   (Japan)

^c ESSI   (France)

Author keywords

Self dual codes; Shadows; Unimodular lattices

Indexed keywords

EID: 0037711148     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(99)00368-4     Document Type: Article

References (18)

1. E. Bannai, S.T. Dougherty, M. Harada, M. Oura, Type II codes, even unimodular lattices and invariant rings, IEEE Trans. Inform. Theory 45 (1999) 1194-1205.
2. R. Bacher, B.B. Venkov, Réseaux entiers unimodulaires sans racine en dimension 27 et 28 (preprint).
3. A. Bonnecaze, A.R. Calderbank, P. Solé, Quaternary quadratic residue codes and unimodular lattices, IEEE Trans. Inform. Theory 41 (1995) 366-377.
4. 4, Discrete Math., to appear.
5. 4, IEEE Trans. Inform. Theory 43 (1997) 969-976.
6. R.E. Borcherds, The Leech lattices and other lattices, Ph.D. Dissertation, Univ. of Cambridge, 1984.
7. R.A. Brualdi, V.S. Pless, Weight enumerators of self-dual codes, IEEE Trans. Inform. Theory 37 (1991) 1222-1225.
8. J.H. Conway, N.J.A. Sloane, A new upper bound on the minimum distance of self-dual codes, IEEE Trans. Inform. Theory 36 (1990) 1319-1333.
9. J.H. Conway, N.J.A. Sloane, A new upper bound for the minimum of an integral lattice of determinant 1, Bull. Amer. Math. Soc. 23 (1990) 383-387.
10. J.H. Conway, N.J.A. Sloane, Sphere Packing, Lattices and Groups, 3rd Edition, Springer, New York, 1999.
11. J.H. Conway, N.J.A. Sloane, A note on optimal unimodular lattices, J. Number Theory 72 (1998) 357-362.
12. S.T. Dougherty, M. Harada, Shadow optimal self-dual codes, Kyushu Math. J. 53 (1999) 223-237.
13. 4, Finite Fields and Their Appl., to appear.
14. N. Elkies, Lattices and codes with long shadows, Math. Res. Lett. 2 (1995) 643-651.
15. 4, Des. Codes and Cryptogr., to appear.
16. 4-codes, Finite Fields Their Appl. 3 (1997) 48-69.
17. 4, submitted for publication.
18. N.J.A. Sloane, G. Nebe, A catalogue of lattices, published electronically at http://www.research. att.com/~njas/lattices/.