A005866 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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

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.

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).

KEYWORD

nonn,hard,nice

AUTHOR

EXTENSIONS

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

STATUS

approved