I've just recently become a fan of your cyclic codes, so I wasn't expecting this. What structure are you highlighting? With just a little messing around I found a 36 element n=9, k=4 code by cycling {0,0,0,0,0,0,0,0,1} {0,0,0,0,0,1,0,1,1} {0,0,0,0,1,0,1,0,1} {0,0,0,0,1,1,0,0,1} giving rate (1/9)log_2(36/4) = 0.352214 and missing Michael's record by .00014 -- rats! -Veit On Nov 29, 2012, at 11:53 AM, Thomas Colthurst <thomaswc@gmail.com> wrote:
The n=6 and n=8 patterns can be re-arranged (per permuting rows and columns) into
n=6: 000 000
001 001 010 010 100 100
001 110 010 101 100 011
111 000
n=8: 0000 0000
0001 0001 0010 0010 0100 0100 1000 1000
0001 1010 0010 1100 0100 1001
1010 0001 1100 0010 1001 0100
0000 0111 0111 0000
I've been playing with these because I really want to find an unique union code for n=15 of size >1000 (i.e., show that you can uniquely identify the two poisoned wine bottles with only 15 bottles).
-Thomas C