Identifying Codes in the Binary Hamming Space

==> Last modified: Thu Nov 26 12:15:43 CET 2009 <==

This page explicitly gives our best r-identifying codes
in the binary Hamming space of dimension n, for various values of r and n.
The constructions refer to
I. Charon, G. Cohen, O. Hudry & A. Lobstein,
New Identifying Codes in the Binary Hamming Space,
European Journal of Combinatorics, vol. 31, pp. 491-501, 2010.

r=1 n=8: 61 codewords           r=1 n=9: 112 codewords            r=1 n=10: 208 codewords
r=1 n=12: 684 codewords       r=1 n=13: 1280 codewords        r=1 n=14: 2550 codewords    
r=1 n=15: 4787 codewords     r=1 n=16: 9494 codewords        r=1 n=17: 18558 codewords    
r=1 n=18: 35604 codewords   r=1 n=20: 131072 codewords     r=1 n=21: 262144 codewords

r=2 n=9: 32 codewords           r=2 n=10: 57 codewords         r=2 n=11: 100 codewords
r=2 n=12: 177 codewords       r=2 n=13: 318 codewords       r=2 n=14: 566 codewords
r=2 n=15: 1020 codewords     r=2 n=16: 1844 codewords     r=2 n=17: 3476 codewords
r=2 n=18: 6430 codewords     r=2 n=19: 12458 codewords   r=2 n=20: 25401 codewords
r=2 n=21: 50342 codewords

r=3 n=5: 10 codewords         r=3 n=6: 7 codewords             r=3 n=7: 8 codewords
r=3 n=8: 13 codewords         r=3 n=9: 17 codewords           r=3 n=10: 25 codewords
r=3 n=11: 36 codewords       r=3 n=12: 67 codewords         r=3 n=13: 109 codewords
r=3 n=14: 180 codewords     r=3 n=15: 305 codewords       r=3 n=16: 530 codewords
r=3 n=17: 901 codewords     r=3 n=18: 1628 codewords     r=3 n=19: 2846 codewords
r=3 n=20: 5813 codewords   r=3 n=21: 11477 codewords

r=4 n=6: 18 codewords         r=4 n=7: 14 codewords         r=4 n=8: 13 codewords
r=4 n=9: 14 codewords         r=4 n=10: 16 codewords       r=4 n=11: 20 codewords
r=4 n=12: 33 codewords       r=4 n=13: 47 codewords       r=4 n=14: 76 codewords
r=4 n=15: 123 codewords     r=4 n=16: 192 codewords     r=4 n=17: 305 codewords
r=4 n=18: 511 codewords     r=4 n=19: 835 codewords     r=4 n=20: 1710 codewords
r=4 n=21: 3358 codewords

r=5 n=7: 32 codewords           r=5 n=8: 21 codewords         r=5 n=9: 17 codewords
r=5 n=10: 16 codewords         r=5 n=11: 17 codewords       r=5 n=12: 22 codewords
r=5 n=13: 26 codewords         r=5 n=14: 43 codewords       r=5 n=15: 64 codewords
r=5 n=16: 94 codewords         r=5 n=17: 136 codewords     r=5 n=18: 210 codewords
r=5 n=19: 326 codewords       r=5 n=20: 663 codewords     r=5 n=21: 1310 codewords