A029866: Size of minimal binary covering code of length n and covering radius 2. 
Best known solutions for n <= 11.

By Dmitry Kamenetsky, 27/07/2020.


a(2)=1
(01)

a(3)=2
(011, 110)

a(4)=2
(0111, 1010)

a(5)=2
(01001, 10110)

a(6)=4
(010101, 011110, 100010, 101001)

a(7)=7
(0010111, 0011011, 0100000, 1001100, 1010011, 1101100, 1111111)

a(8)=12
(00001001, 00010111, 00101100, 01010010, 01101011, 01110100, 10000010, 10011101, 10111110, 11001010, 11100101, 11110001)

a(9)=16
(000000100, 000111101, 001001011, 001110010, 010010001, 010011110, 011100111, 011101000, 100100001, 100101110, 101010111, 101011000, 110000010, 110111011, 111001101, 111110100)

a(10)<=30
(0000001010, 0000110101, 0001000101, 0010010001, 0010100111, 0010111111, 0011010111, 0011100001, 0011111001, 0100001011, 0100101100, 0101011100, 0101110010, 0110001000, 0111001110, 1000001011, 1000101000, 1001101110, 1001111011, 1010011101, 1011001010, 1100010110, 1100101001, 1101010000, 1101101111, 1110000100, 1110110010, 1111001011, 1111101100, 1111110100)

a(11)<=44
(00000010011, 00001000101, 00001011001, 00010001110, 00011010000, 00100100111, 00100111011, 00101101101, 00101110001, 00110110010, 00111100100, 00111111000, 01000101000, 01001100010, 01001111110, 01010110101, 01011101011, 01100000000, 01100011100, 01101001111, 01101010110, 01110001001, 01111000011, 01111011111, 10000110100, 10001101010, 10010100001, 10010111101, 10011110111, 10100001000, 10101000010, 10101011110, 10110010101, 10111001011, 11000001111, 11001010001, 11010000110, 11010011010, 11011001100, 11100110011, 11101100101, 11101111001, 11110101110, 11111110000)