I'm trying to create error correction code for small binary strings.
My space = all words with
X bits (
Y = 2^X words total).
I want to transform my space to a new space with the same amount of words -
Y but, each word represented by
X+Z bits and each word in the new space has hamming distance
For example, my space is
00 - 01 - 10 - 11
and I decided
d=2, so the new space is:
0000 - 0101 - 1010 - 0011
So I know I can correct 1 error which is 25% of the data. My goal is to correct ~30% with minimum headers.
1. What is the max Hamming distance for between
Y words with
2. How do I know if such transform exists?
3. If it exists, how do I find
Z and the transform function?