NAME 1 BEST.12.144.4 TYPE 1 101 LINEAR 1 0 FIELD 1 2 LENGTH 1 12 SIZE 1 144 NOTES 16 This was "Julinc" The (12,144,4) code found by Best that has the (10,40,4) code as a subcode (delete coords 1 and 6) - see L9 p 156, Best's report p 16. Remarks: this does not contain a Steiner System S(5,6,12) Proof: Compare the distance dnbs of these words (given below) with the dist dbn of the S(5,6,12), which is no of wt dists is 1 dist no 1 occurred 132 times 1 2 3 4 5 6 7 8 9 10 11 12 0 0 0 45 0 40 0 45 0 0 0 1 There is no subset of 132 words of the 144 with this distance dbn. QED BOOK 144 110010100000 110001010000 110000001010 110000000101 101100100000 101001001000 101000010001 101000000110 100101000100 100100011000 100100000011 100011000010 100010010100 100010001001 100001100001 100000110010 100000101100 011100000010 011010000100 011000110000 011000001001 010110001000 010100100100 010100010001 010011000001 010010010010 010001101000 010001000110 010000100011 010000011100 001110010000 001101000001 001100001100 001010101000 001010000011 001001100010 001001010100 001000100101 001000011010 000110100010 000110000101 000101110000 000101001010 000100101001 000100010110 000011100100 000011011000 000010110001 000010001110 000001010011 000001001101 001101011111 001110101111 001111110101 001111111010 010011011111 010110110111 010111101110 010111111001 011010111011 011011100111 011011111100 011100111101 011101101011 011101110110 011110011110 011111001101 011111010011 100011111101 100101111011 100111001111 100111110110 101001110111 101011011011 101011101110 101100111110 101101101101 101110010111 101110111001 101111011100 101111100011 110001101111 110010111110 110011110011 110101010111 110101111100 110110011101 110110101011 110111011010 110111100101 111001011101 111001111010 111010001111 111010110101 111011010110 111011101001 111100011011 111100100111 111101001110 111101110001 111110101100 111110110010 000000000000 111111111111 000000111111 000011101011 000101100111 000110011011 000110111100 001001111001 001010011101 001010110110 001100110011 001111000110 010001110101 010010101101 010100001111 010100111010 010111010100 011000010111 011000101110 011011001010 011101011000 011110100001 111111000000 111100010100 111010011000 111001100100 111001000011 110110000110 110101100010 110101001001 110011001100 110000111001 101110001010 101101010010 101011110000 101011000101 101000101011 100111101000 100111010001 100100110101 100010100111 100001011110 WTDN 30 The dist dnbs: no of wt dists is 4 dist no 1 occurred 24 times 1 2 3 4 5 6 7 8 9 10 11 12 0 0 0 43 0 56 0 43 0 0 0 1 dist no 2 occurred 32 times 1 2 3 4 5 6 7 8 9 10 11 12 0 0 0 47 0 48 0 47 0 0 0 1 dist no 3 occurred 80 times 1 2 3 4 5 6 7 8 9 10 11 12 0 0 0 45 0 52 0 45 0 0 0 1 dist no 4 occurred 8 times 1 2 3 4 5 6 7 8 9 10 11 12 0 0 0 51 0 40 0 51 0 0 0 1 NOTES 247 Here are the 22 "extra" words from Best's report for code # 16 p 26 followed by their complements 000000111111 000001111110 000011101011 000101100111 000110011011 000110111100 001001111001 001010011101 001010110110 001100110011 001111000110 010001110101 010010101101 010100001111 010100111010 010111010100 011000010111 011000101110 011011001010 011101011000 011110100001 011111100000 111111000000 111110000001 111100010100 111010011000 111001100100 111001000011 110110000110 110101100010 110101001001 110011001100 110000111001 101110001010 101101010010 101011110000 101011000101 101000101011 100111101000 100111010001 100100110101 100010100111 100001011110 100000011111 Here are the words after applying a perm to put the 2 special coords at the end: wt2.f. n,d,w,m,ifind= 12 4 4 144 0 the perm 2 3 4 5 7 8 9 10 11 12 1 6 100110000010 100001000011 100000101010 100000010110 011010000010 010000100011 010001000110 010000011010 001000010011 001001100010 001000001110 000100001011 000101010010 000100100110 000010000111 000011001010 000010110010 111000001000 110100010000 110011000000 110000100100 101100100000 101010010000 101001000100 100100000101 100101001000 100010100001 100000011001 100010001100 100001110000 011101000000 011000000101 011000110000 010110100000 010100001100 010010001001 010001010001 010010010100 010001101000 001110001000 001100010100 001011000001 001000101001 001010100100 001001011000 000110010001 000101100001 000111000100 000100111000 000001001101 000000110101 011001111101 011110111100 011111010101 011111101001 100101111101 101111011100 101110111001 101111100101 110111101100 110110011101 110111110001 111011110100 111010101101 111011011001 111101111000 111100110101 111101001101 000111110111 001011101111 001100111111 001111011011 010011011111 010101101111 010110111011 011011111010 011010110111 011101011110 011111100110 011101110011 011110001111 100010111111 100111111010 100111001111 101001011111 101011110011 101101110110 101110101110 101101101011 101110010111 110001110111 110011101011 110100111110 110111010110 110101011011 110110100111 111001101110 111010011110 111000111011 111011000111 111110110010 111111001010 000000000000 111111111111 000011111100 000110101101 001010011101 001101101100 001111110000 010011100101 010101110100 010111011000 011011001100 011100011001 100011010101 100110110100 101000111100 101011101000 101101010001 110001011100 110010111000 110100101001 111001100001 111110000100 111100000011 111001010010 110101100010 110010010011 110000001111 101100011010 101010001011 101000100111 100100110011 100011100110 011100101010 011001001011 010111000011 010100010111 010010101110 001110100011 001101000111 001011010110 000110011110 000001111011 no of wt dists is 4 Here are the 40 words of the shortened code: wt2.f. n,d,w,m,ifind= 10 4 4 40 0 1110000010 1101000100 1100110000 1100001001 1011001000 1010100100 1010010001 1001010010 1000100011 1000011100 0111010000 0110001100 0101101000 0101000011 0100100101 0100011010 0011100010 0011000101 0010101001 0010010110 0001110001 0001001110 0111101111 1011110111 1101111011 1110111101 1111011110 0000000000 0000111111 0011011011 0011111100 0101011101 0101110110 0110110011 1001101101 1010001111 1010111010 1100010111 1100101110 1111100001 no of wt dists is 1 dist no 1 occurred 40 times 1 2 3 4 5 6 7 8 9 10 0 0 0 22 0 12 0 5 0 0 ZZZZ