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

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

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice
• more

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

• 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).

Extensions

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