A105675 Highest minimal distance of any Type II doubly-even binary self-dual code of length 8n.

4, 4, 8, 8, 8, 12, 12, 12

Offset

1,1

Comments

Is a(9) = 12 or 16? This is an open question of long standing.

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977.

Links

Table of n, a(n) for n=1..8.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

P. Gaborit, Tables of Self-Dual Codes

E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998; (Abstract, pdf, ps).

N. J. A. Sloane, Is There a (72,36) d = 16 Self-Dual Code?, IEEE Trans. Information Theory, vol. IT-19 (1973), p. 251.

Example

At length 8 the only Type II doubly-even self-dual code is the Hamming code e_8, which has d=4, so a(1) = 4. The [24,12,8] Golay code has d=8, so a(3) = 8.

Crossrefs

Cf. A105674, A105676, A105677, A105678, A016729, A066016, A105681, A105682.

Cf. also A001380, A018236.

Sequence in context: A333167 A246066 A076359 * A196054 A292135 A053249

Adjacent sequences: A105672 A105673 A105674 * A105676 A105677 A105678

Keyword

nonn,hard,more,nice

Author

N. J. A. Sloane, May 06 2005

Status

approved