# Galois Field implementation

Just a quick question. What Galois Field is best if you need a minimum Hamming distance of $n$? I want to design a BCH generator polynomial that is acccording to this Hamming distance.

• @LeBlancLord See the first page of the first link which outlines the block length n, the number of parity bits and minimum distance for a t-error corecting BCH code. In your case t=3, the minimum distance is >=7 and the number of parity-check digits is <= mt where the block length = $2^m-1$. With t small, n-k is exactly mt. So solving this for t=3 and k=16 results in m=5. So if I did that correctly you would have 16 message bits, and 3m=15 parity bits for a block length of 31, and dmin is 2t+1=7. Do you agree? – Dan Boschen May 10 '17 at 9:43