On the dimensions of certain LDPC codes based on q-regular bipartite graphs
An explicit construction of a family of binary low-density parity check (LDPC) codes called LU(3, q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The proof involves the geometry of a four-dimensional (4-D) symplectic vector space and the action of the symplectic group and its subgroups.
low-density parity check (ldpc) code generalized quadrangle incidence matrix symplectic grou