A000983: Size of minimal binary covering code of length n and covering radius 1. 
Best known solutions for n <= 11.

By Dmitry Kamenetsky, 27/07/2020.


a(1)=1
(1)

a(2)=2
(00, 10)

a(3)=2
(011, 100)

a(4)=4
(0001, 0101, 1010, 1110)

a(5)=7
(00000, 00001, 00010, 01111, 10111, 11011, 11100)

a(6)=12
(000011, 000100, 001010, 011001, 011101, 011111, 100101, 101011, 101100, 110000, 110010, 110110)

a(7)=16
(0000011, 0001110, 0010000, 0011101, 0100100, 0101001, 0110111, 0111010, 1000101, 1001000, 1010110, 1011011, 1100010, 1101111, 1110001, 1111100)

a(8)=32
(00010110, 10110001, 11000010, 00111111, 11111100, 10101110, 11100101, 00001011, 00000001, 10101000, 00011000, 10001101, 01111010, 11011001, 00100010, 01010011, 01010101, 00111101, 11011111, 01110000, 11101011, 01101001, 11000000, 01001100, 00100100, 10010100, 10011010, 11110110, 01100111, 10000111, 01001110, 10110011)

a(9)=62
(000000000, 000000010, 000000100, 000010111, 000011011, 000100000, 000101110, 000110011, 000111101, 001001001, 001010011, 001011000, 001011111, 001100110, 001101100, 001101110, 001110101, 001111011, 010001111, 010010001, 010011100, 010100111, 010101001, 010110100, 010111010, 011000101, 011001010, 011010110, 011100011, 011110000, 011111101, 100001101, 100010001, 100011110, 100100101, 100101011, 100110110, 100111000, 101000111, 101001010, 101010100, 101100001, 101110010, 101111101, 110000011, 110000110, 110001000, 110010010, 110010101, 110100010, 110101100, 110110001, 110111111, 111000000, 111001100, 111011001, 111011011, 111100100, 111101000, 111101111, 111110111, 111111110)

a(10)<=120
(0000000011, 0000001110, 0000011000, 0000101001, 0000110100, 0000111111, 0001000101, 0001010110, 0001011011, 0001100010, 0001101100, 0001110001, 0010001100, 0010001101, 0010001111, 0010010011, 0010011101, 0010101010, 0010111010, 0010111101, 0011000000, 0011010000, 0011011000, 0011100011, 0011100110, 0011100111, 0011110110, 0011110111, 0100000000, 0100010101, 0100011011, 0100100111, 0100101100, 0100110010, 0101001001, 0101001010, 0101001111, 0101010011, 0101011100, 0101100100, 0101101011, 0101111000, 0101111101, 0101111110, 0110000001, 0110000110, 0110010100, 0110010110, 0110100000, 0110100001, 0110110001, 0110111010, 0111001010, 0111001011, 0111011111, 0111101100, 0111101101, 0111110001, 0111111001, 0111111100, 1000000100, 1000001011, 1000010001, 1000010010, 1000010111, 1000100000, 1000100101, 1000100110, 1000110011, 1000111100, 1001000011, 1001001000, 1001011101, 1001101111, 1001110100, 1001111010, 1010000010, 1010000011, 1010010011, 1010011110, 1010100100, 1010100101, 1010110000, 1010110100, 1011001001, 1011001110, 1011010101, 1011011110, 1011101000, 1011101001, 1011111001, 1011111011, 1100000011, 1100001101, 1100011110, 1100101010, 1100110100, 1100111001, 1101000110, 1101010000, 1101011011, 1101100001, 1101101100, 1101110111, 1110001000, 1110011000, 1110011001, 1110101011, 1110101110, 1110101111, 1110110111, 1110111111, 1111000100, 1111000101, 1111000111, 1111010010, 1111010101, 1111100010, 1111110010, 1111111100)

a(11)<=192
(00000000110, 00000001001, 00000011010, 00000101111, 00000110101, 00001000011, 00001010100, 00001101100, 00001110010, 00001111001, 00010001100, 00010010001, 00010011111, 00010100011, 00010110110, 00010111000, 00011000000, 00011001111, 00011010111, 00011011111, 00011100101, 00011101010, 00100000101, 00100010000, 00100101010, 00100110011, 00100111100, 00101001000, 00101011011, 00101011101, 00101011110, 00101100001, 00101100110, 00101111111, 00110000010, 00110001111, 00110010111, 00110011111, 00110100100, 00110101001, 00111000111, 00111001111, 00111010111, 00111011001, 00111011010, 00111011100, 00111110000, 00111111011, 00111111101, 00111111110, 01000000000, 01000010011, 01000011101, 01000100010, 01000100100, 01000110000, 01000111110, 01001000101, 01001001110, 01001011000, 01001101011, 01001110111, 01010000111, 01010001010, 01010010100, 01010100000, 01010101101, 01010111011, 01011001001, 01011010010, 01011011111, 01011100110, 01011110001, 01011111100, 01100001011, 01100001100, 01100010110, 01100100111, 01100111001, 01101000010, 01101010001, 01101101101, 01101110100, 01101111010, 01110000001, 01110011000, 01110011111, 01110101110, 01110110010, 01110110101, 01111000100, 01111001111, 01111010111, 01111011111, 01111100011, 01111101000, 10000010111, 10000011100, 10000100000, 10000100001, 10000101000, 10000111011, 10001001010, 10001001101, 10001010001, 10001100000, 10001100111, 10001111110, 10010000101, 10010001011, 10010010010, 10010101110, 10010111101, 10011000110, 10011011000, 10011101001, 10011110011, 10011110100, 10100000011, 10100001110, 10100011001, 10100100000, 10100101101, 10100110110, 10101000100, 10101010010, 10101011111, 10101101011, 10101110101, 10101111000, 10110001000, 10110010100, 10110100111, 10110110001, 10110111010, 10111000001, 10111011011, 10111011101, 10111011110, 10111100010, 10111101100, 10111111111, 11000000010, 11000000100, 11000001111, 11000010000, 11000100001, 11000100110, 11000101000, 11000101001, 11000110010, 11000110100, 11001010110, 11001011011, 11001100000, 11001100001, 11001101000, 11001111101, 11010000000, 11010011001, 11010011110, 11010100010, 11010100100, 11010110000, 11010110111, 11011000011, 11011001100, 11011010101, 11011101111, 11011111010, 11100010101, 11100011010, 11100100000, 11100100001, 11100101000, 11100111111, 11101000111, 11101001001, 11101011100, 11101100000, 11101101110, 11101110011, 11110000110, 11110001101, 11110010011, 11110101011, 11110111100, 11111001010, 11111010000, 11111100101, 11111110110, 11111111001)