A004045 - OEIS

%I #28 Mar 03 2020 23:38:39

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

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

%H H. Hamalainen et al., <a href="http://www.jstor.org/stable/2974552">Football pools - a game for mathematicians</a>, Amer. Math. Monthly, 102 (1995), 579-588.

%e From _Paul Tabatabai_, Mar 02 2020: (Start)

%e Lexicographically first optimal code for n = 6:

%e 0 1 2 4 8 23 27 29 30 31 39 43 45 46 47 48 49 50 52 56.

%e Lexicographically first optimal code for n = 7:

%e 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)

%K nonn,hard,more

%O 1,1

%A _N. J. A. Sloane_

%E a(6)-a(7) from _Paul Tabatabai_, Mar 02 2020