Binary LDPC Codes Constructed Based on Symplectic Spaces over Finite Fields

Abstract

This paper mainly presents a construction of LDPC codes based on symplectic spaces. By two subspaces of type (m, r) to produce a subspace of type (m + 1,r) or (m + 1,r + 1) in ${\mathbb{F}}^{2v}$ , we use all subspaces of type (m,r) to mark rows and all subspaces of type (m + 1, r) and (m + 1, r + 1) to mark columns of check matrix H. A construction of LDPC codes has been given based on symplectic spaces. As a special case, we use all subspaces of type (1,0) to mark rows and all subspaces of type (2,0) and (2,1) to mark columns of check matrix $H_1$, in ${\mathbb{F}}_q^4$, the cycles of length 6 of $H_1$, is further discussed.