Construction of Extremal Type II Codes over ℤ4

Designs, Codes, and Cryptography

Volumn 16, Issue 3, 1999, Pages 257-269

  Gaborit, Philippe ^a   Harada, Masaaki ^b  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b YAMAGATA UNIVERSITY   (Japan)

Author keywords

Extremal codes and type II codes; Self dual codes over 4

Indexed keywords

EID: 0345771910     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008335912135     Document Type: Article

References (22)

1. A. Bonnecaze, P. Solé and A.R. Calderbank, Quaternary quadratic residue codes and unimodular lattices, IEEE Trans. Inform. Theory, Vol. 41 (1995) pp. 366-377.
2. 4, IEEE Trans. Inform. Theory, Vol. 43 (1997) pp. 969-976.
3. 4, locator polynomials, and Newton identities, IEEE Trans. Inform. Theory Vol. 42 (1996) pp. 217-226.
4. 4 and even unimodular lattices, J. Alg. Combin., Vol. 6 (1997) pp. 119-131.
5. P. J. Cameron and J. H. van Lint, Designs, Graphs, Codes and Their Links, Cambridge University Press, Cambridge (1991).
6. R. Chapman and P. Solé, Universal codes and unimodular lattices, J. de th. des nombres de Bordeaux, Vol. 8 (1996) pp. 369-376.
7. J. H. Conway and N. J. A. Sloane, Self-dual codes over the integers modulo 4, J. Combin. Theory Ser. A Vol. 62 (1993) pp. 30-45.
8. J. H. Conway and N. J. A. Sloane, Sphere Packing, Lattices and Groups (2nd ed.), Springer-Verlag, New York (1993).
9. J. H. Conway and V. Pless, On the enumeration of self-dual codes, J. Combin. Theory Ser. A, Vol. 28 (1980) pp. 26-53.
10. J. H. Conway, V. Pless and N. J. A. Sloane, The binary self-dual codes of length up to 32: a revised enumeration, J. Combin. Theory Ser. A, Vol. 60 (1992) pp. 183-195.
11. 4 codes of length 15 or less are known , IEEE Trans. Inform. Theory, Vol. 44 (1998) pp. 311-323.
12. q rings, IEEE Trans. Inform. Theory, Vol. 42 (1996) pp. 1222-1228.
13. 4 and construction of 5-(24, 10, 36) designs, Discrete Math., Vol. 194 (1999) pp. 129-137.
14. 4, Des. Codes and Cryptogr., Vol. 13 (1998) pp. 271-284.
15. 4, J. Combin. Designs, Vol. 6 (1998) pp. 225-229.
16. 4, IEEE Trans. Inform. Theory, Vol. 44 (1998) pp. 800-809.
17. 4 Type II codes of length 16 are known, J. Combin. Theory Ser. A, Vol. 78 (1997) pp. 32-50.
18. 4-codes, Finite Fields Their Appl., Vol. 3 (1997) pp. 48-69.
19. E. Rains, private communication, November 4, 1997.
20. 4, preprint, November 1997.
21. V.D. Tonchev, Block designs of Hadamard type and self-dual codes, Probl. Perda. Inform., Vol. 19 (1983) pp. 25-30 (in Russian). English translation in: Probl. Inform. Transm., Vol. 19 (1984) pp. 270-275.
22. V.D. Tonchev, Block designs of Hadamard type and self-dual codes, Probl. Perda. Inform., Vol. 19 (1983) pp. 25-30 (in Russian). English translation in: Probl. Inform. Transm., Vol. 19 (1984) pp. 270-275.