LDPC Codes Based On The Space Of Hermitian Matrices

Let 2 denote the finite field with q2 elements, where q is a power of a prime. Let V(n, q2) be the set of all n x n Hermitian matrices over Fq2 and L(n,q2)={lH,K|H,K∈ V(n,q2),rank(H　-　K)= 1}, whose elements are called points and lines respectively, where lH,k={H+k(K -H)| k ∈ Fg}. The incident relation of the points and lines is relation of inclusion. (V(n, q2),L(n, q2)) constitute a bipartite graph T(n,q2). Let H(n,q2) be the incidence matrix of T(n,q2), where the rows are indexed by lines and columns are indexed by points. The binary code with the parity check matrix H(n, q2) is an LDPC code, denoted by C(n, q2). Let d be the minimum distance of C(2, q2), we have 2q2 + 2q + 4< d< 2q3, where n= 2, q is a power of 2 and q> 2. If q= 2 the minimum distance of C(2,4) is 16.The binary code with the parity check matrix H’(n,q2) is also an LDPC code, de noted by C’(n, q2). If n= 2 the minimum distance of C’(2, q2) is 2q, where q is a powei of 2.