LDPC Codes Based on the Space of Symmetric Matrices Over Finite Fields

In this paper, we present a new method for explicitly constructing regular low-density parity-check (LDPC) codes based on Sn(Fq), the space of n × n symmetric matrices over Fq. Using this method, we obtain two classes of binary LDPC codes, C(n, q) and CT (n, q), both of which have grith 8. Then, both the minimum distance and the stopping distance of each class are investigated. It is shown that the minimum distance and the stopping distance of C
^T
(n, q) are both 2q. As for C(n, q), we determine the minimum distance and the stopping distance for some special cases and obtain some lower bounds for other cases.