On the rank of LDPC matrices constructed by Vandermonde matrices and RS codes

We calculate the rank of low-density parity-check (LDPC) matrices based on Vandermonde matrix like constructions. In the case of prime fields the rank is given exactly. We show that LDPC codes based on RS codes are a special case of the Vandermonde based construction, thus also for these LDPC matrix construction, the rank calculation is valid. However, for extension fields the calculation is more sophisticated because of the nilpotent property of the parity check matrix. Therefore we can give presently only a bound for the rank in case of binary extension fields