A005865 The coding-theoretic function A(n,6).

1, 1, 1, 1, 1, 2, 2, 2, 4, 6, 12, 24, 32, 64, 128, 256

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice
• more

Comments

Since A(n,5) = A(n+1,6), A(n,5) gives essentially the same sequence.

The next term is known only to be in the range 258-340. - Moshe Milshtein, Apr 24 2019

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, Tables of general binary codes
• 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.
• M. Grassl, Bounds on the minimum distance of linear codes
• Moshe Milshtein, A new two-error-correcting binary code of length 16, Cryptography and Communications (2019).
• Eric Weisstein's World of Mathematics, Error-Correcting Code.
• Index entries for sequences related to A(n,d)

Crossrefs

Cf. A005864, A005866, A169761, A169762.