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

Author

N. J. A. Sloane, May 06 2005

Keywords

• nonn
• hard
• more
• nice

Comments

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

Examples

			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.
		

References

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

Links

• 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.

Crossrefs

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

Cf. also A001380, A018236.