A070979 Triangle read by rows giving size of minimal asymmetric covering code of length n and radius R.

1, 2, 1, 3, 2, 1, 6, 3, 2, 1, 10, 5, 3, 2, 1, 18, 8, 4, 3, 2, 1, 31

Offset

1,2

Comments

Minimal binary code C of length n such that every vector of length n can be obtained from a codeword by changing at most R 1's to 0's.

Links

Table of n, a(n) for n=1..22.

D. Applegate, E. M. Rains and N. J. A. Sloane, On asymmetric coverings and covering numbers, J. Comb. Des. 11 (2003), 218-228.

J. N. Cooper, R. B. Ellis and A. B. Kahng, Asymmetric binary covering codes, J. Comb. Theory Ser. A, Vol. 100, no. 2 (2002), 232-249.

R. B. Ellis, Asymmetric Covering Codes. [Dead link]

Example

n=5, R=2: C={11111,01111,10011,11100,00011}.
Triangle begins:
   1;
   2, 1;
   3, 2, 1;
   6, 3, 2, 1;
  10, 5, 3, 2, 1;
  18, 8, 4, 3, 2, 1;
  31 ...

Crossrefs

Cf. A066000, A019436.

Sequence in context: A308701 A191528 A191788 * A363272 A054098 A132089

Adjacent sequences: A070976 A070977 A070978 * A070980 A070981 A070982

Keyword

nonn,tabl,nice,hard,more

Author

Joshua N. Cooper (jcooper(AT)math.ucsd.edu), May 17 2002

Status

approved