A005866 The coding-theoretic function A(n,8). (Formerly M0226)

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 8, 16, 32, 36, 64, 128, 256, 512, 1024, 2048, 4096

Offset

1,8

Comments

Since A(n,7) = A(n+1,8), A(n,7) gives essentially the same sequence.

The next term, A(25,8), is known to be at least 4096 and at most 5421. - Moshe Milshtein, Dec 03 2018

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 248.

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 674.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..24.

A. E. Brouwer, Small binary codes: Table of general binary codes, personal web page.

A. E. Brouwer, J. B. Shearer, N. J. A. Sloane and W. D. Smith, New table of constant weight codes, IEEE Trans. Info. Theory 36 (1990), 1334-1380.

Patric R. J. Östergård, On the Size of Optimal Three-Error-Correcting Binary Codes of Length 16, IEEE Transactions on Information Theory, Volume 57, Issue 10, Oct. 2011.

N. J. A. Sloane and D. S. Whitehead, A New Family of Single-Error Correcting Codes [Shows a(18) >= 36.]

Eric Weisstein's World of Mathematics, Error-Correcting Code.

Index entries for sequences related to A(n,d)

Crossrefs

Cf. A005864: A(n,4) and A(n,3), A005865: A(n,6) and A(n,5).

Cf. A005851: A(n,8,5), A005852: A(n,8,6), A005853: A(n,8,7), A004043: A(n,8,8).

Sequence in context: A328583 A355537 A240674 * A125584 A230447 A029078

Adjacent sequences: A005863 A005864 A005865 * A005867 A005868 A005869

Keyword

nonn,hard,nice

Author

N. J. A. Sloane

Extensions

a(18)-a(24) from Moshe Milshtein, Dec 03 2018

Status

approved