LDPC Codes from Projective Algebraic Sets over Finite Fields

Our main aim is to present a new construction of low-density parity-check (LDPC) codes from projective algebraic sets over finite fields,where the sets are the intersection of a one-dimensional hyperplane with one hypersurface of homogeneous polynomial equation in projective n-space. In particular, for 2-dimensional case, the projective algebraic sets are the intersection of a line with one curve, and the parity-check matrices of the LDPC codes are the incidence matrices of the points and lines which we can see in some well-known papers.