  This paper generalizes the method proposed by Poulliat et al. for the
determination of the optimal Galois Field coefficients of a Non-Binary LDPC
parity check constraint based on the binary image of the code. Optimal, or
almost-optimal, parity check coefficients are given for check degree varying
from 4 to 20 and Galois Field varying from GF(64) up to GF(1024). For all given
sets of coefficients, no codeword of Hamming weight two exists. A reduced
complexity algorithm to compute the binary Hamming weight 3 of a parity check
is proposed. When the number of sets of coefficients is too high for an
exhaustive search and evaluation, a local greedy search is performed. Explicit
tables of coefficients are given. The proposed sets of coefficients can
effectively replace the random selection of coefficients often used in NB-LDPC
construction.
