Cyclic Codes From the Two-Prime Sequences

Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, the two-prime sequence is employed to construct several classes of cyclic codes over GF(q). Lower bounds on the minimum weight of these cyclic codes are developed. Some of the codes obtained are optimal or almost optimal. The p-ranks of the twin-prime difference sets and a class of almost difference sets are computed.