A004045 Minimal size of binary code of length n such that every vector is within distance 1 of at least 2 codewords.

2, 3, 4, 8, 12, 20, 32

Offset

1,1

Links

Table of n, a(n) for n=1..7.

H. Hamalainen et al., Football pools - a game for mathematicians, Amer. Math. Monthly, 102 (1995), 579-588.

Example

From Paul Tabatabai, Mar 02 2020: (Start)
Lexicographically first optimal code for n = 6:
0 1 2 4 8 23 27 29 30 31 39 43 45 46 47 48 49 50 52 56.
Lexicographically first optimal code for n = 7:
0 1 6 7 24 25 30 31 42 43 44 45 50 51 52 53 74 75 76 77 82 83 84 85 96 97 102 103 120 121 126 127. (End)

Crossrefs

Sequence in context: A222124 A222125 A222126 * A060200 A057608 A060984

Adjacent sequences: A004042 A004043 A004044 * A004046 A004047 A004048

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Extensions

a(6)-a(7) from Paul Tabatabai, Mar 02 2020

Status

approved