Some low-density parity-check codes derived from finite geometries

We look at low-density parity-check codes over a finite field K associated with finite geometries T(2)*(K), where K is a sufficiently large k-arc in PG(2, q), with q = p(h). The code words of minimum weight are known. With exception of some choices of the characteristic of K we compute the dimension of the code and show that the code is generated completely by its code words of minimum weight