Type II codes, even unimodular lattices, and invariant rings

IEEE Transactions on Information Theory

Volumn 45, Issue 4, 1999, Pages 1194-1205

  Bannai, Eiichi ^a   Dougherty, Steven T ^a   Harada, Masaaki ^a   Oura, Manabu ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

MATRIX ALGEBRA; THEOREM PROVING;

EVEN UNIMODULAR LATTICES; INVARIANT RINGS; LEECH LATTICE; MACWILLIAMS IDENTITY; MOLIEN SERIES;

BINARY CODES;

EID: 0032690017     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.761269     Document Type: Article

References (24)

1. 4-codes," preprint.
2. A. Bonnecaze, P. Sole, and A. R. Calderbank Quaternary quadratic residue codes and unimodular lattices," IEEE Trans. Inform. Theory, vol. 41, pp. 366-377, 1995.
3. A. Bonnecaze, P. Sole, C. Bachoc, and B. Mourrain Type II codes over Z4," IEEE Trans. Inform. Theory, vol. 43, pp. 969-976, 1997.
4. A. R. Calderbank and N. J. A. Sloane Modular and p-adic cyclic codes," Designs, Codes Cryptogr., vol. 6, pp. 21-35, 1995.
5. 4 and even unimodular lattices," J. Alg. Combin., vol. 6, pp. 119-131, 1997.
6. J. H. Conway and N. J. A. Sloane A new upper bound on the minimal distance of self-dual codes," IEEE Trans. Inform. Theory, vol. 36, pp. 1319-1333, 1990.
7. _, Sphere Packing, Lattices and Groups, 2nd ed. New York: Springer-Verlag, 1993.
8. _ Self-dual codes over the integers modulo 4," J. Combin. Theory Ser. A, vol. 62, pp. 30-45, 1993.
9. S. T. Dougherty, T. A. Gulliver, and M. Harada Type II self-dual codes over finite rings and even unimodular lattices," J. Alg. Combin., to be published.
10. 4," submitted to Finite Fields Their Appl.
11. _ Self-dual codes over rings and the Chinese remainder theorem," Hokkaido Math. J., to be published.
12. W. Duke On codes and Siegel modular forms," Int. Math. Res. Notices, pp. 125-136, 1993.
13. 4 and the odd Leech lattice," in Lecture Notes in Computer Science, vol. 1255. Berlin, Germany: Springer-Verlag, 1997, pp. 130-137.
14. 4-linearity of Kerdock, Preparata, Goethals and related codes," IEEE Trans. Inform. Theory, vol. 40, pp. 301-319, 1994.
15. M. Harada New 5-designs constructed from the lifted Golay code over Z4," J. Combin. Des., vol. 6, pp. 225-229, 1998.
16. 4 and unimodular lattices: A survey," submitted for publication.
17. V. G. Kac, Infinite Dimensional Lie Algebras (Progress in Mathematics). vol. 44. Basel, Switzerland Birkhäuser, 1983.
18. C. L. Mallows and N. J. A. Sloane An upper bound for self-dual codes," Inform. Contr.. vol. 22, pp. 188-200, 1973.
19. O. T. O. O'Meara, Introduction to Quadratic Forms. New York: Springer-Verlag, 1971.
20. M. Oura The dimension formula for the ring of code polynomials in genus 4," Osaka J. Math., vol. 34, pp. 53-72, 1997.
21. E. Rains and N. J. A. Sloane The shadow theory of modular and unimodular lattices," J. Number Theory, to be published.
22. B. Runge On Siegel modular forms, Part II," Nagoya Math. J., vol. 138, pp. 179-197, 1995.
23. _ Codes and Siegel modular forms," Discr. Math., vol. 148, 175-204, 1996.
24. _ Theta functions and Siegel-Jacobi forms," Acta Math., vol. 175, pp. 165-196, 1995.