

A105675


Highest minimal distance of any Type II doublyeven binary selfdual code of length 8n.


19




OFFSET

1,1


REFERENCES

F. J. MacWilliams and N. J. A. Sloane, The Theory of ErrorCorrecting Codes, Elsevier/North Holland, 1977.
N. J. A. Sloane, Is There a (72,36) d = 16 SelfDual Code?, IEEE Trans. Information Theory, vol. IT19 (1973), p. 251.


LINKS

Table of n, a(n) for n=1..8.
G. Nebe, E. M. Rains and N. J. A. Sloane, SelfDual Codes and Invariant Theory, Springer, Berlin, 2006.
P. Gaborit, Tables of SelfDual Codes
E. M. Rains and N. J. A. Sloane, Selfdual codes, pp. 177294 of Handbook of Coding Theory, Elsevier, 1998; (Abstract, pdf, ps).


EXAMPLE

At length 8 the only Type II doublyeven selfdual 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: A016712 A246066 A076359 * A196054 A292135 A053249
Adjacent sequences: A105672 A105673 A105674 * A105676 A105677 A105678


KEYWORD

nonn,hard,nice


AUTHOR

N. J. A. Sloane, May 06 2005


EXTENSIONS

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


STATUS

approved



