30 May
2006
30 May
'06
11:32 p.m.
Certain codes (Hamming codes, e.g.) break the code words into a data portion and a parity portion. You could try having the data portion consist of all possible non-stuttering sequences that don't start with 0, which allows you to treat it as a number in 1 .. 3^m for the purposes of the parity portion. For example, if you had 2 data dimensions and one parity dimension, you would start from the code prefixes { 10, 12, 13, 20, 21, 23, 30, 31, 32 }. To get 23's parity dimension, you could take its position (6 of 9), reduce it mod 3 (0), and then append it using the x -> last digit +x+1 mod 4 mapping to get the final codword of 230. -Thomas C