Cyclic codes from cyclotomic sequences of order four

Cyclic codes are a subclass of linear codes and have a lot of applications in consumer electronics, data transmission technologies, broadcast systems, and computer applications as they have efficient encoding and decoding algorithms. In this paper, three cyclotomic sequences of order four are employed to construct a number of classes of cyclic codes over GF(q) with prime length. Under certain conditions lower bounds on the minimum weight are developed. Some of the codes obtained are optimal or almost optimal. In general, the codes constructed in this paper are very good. Some of the cyclic codes obtained in this paper are closely related to almost difference sets and difference sets.