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 CT(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.

Cyclic codes with two zeros and their dual codes have been a subject of study for many years. However, their weight distributions are known only for a few cases. In this paper, the weight distributions of the duals of the cyclic codes with two zeros are settled for a few more cases.

Cyclic codes with two zeros and their dual codes have been a subject of study for many years. However, their weight distributions are known only for a few cases. In this paper, the weight distributions of the duals of the cyclic codes with two zeros are settled for a few cases. The weight distributions of punctured versions of these codes are also determined for several special cases.