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.
dimension ldpc error rate linear representation generalized quadrangle lu(3, q)