Cyclic Codes from Dickson Polynomials

Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer electronics, and data storage systems. In this paper, Dickson polynomials of the first kind over finite fields are employed to construct a number of classes of cyclic codes. Lower bounds on the minimum weight of some classes of the cyclic codes are developed. The minimum weights of some other classes of the codes constructed in this paper are determined. The dimensions of the codes obtained in this paper are flexible. Many of the codes presented in this paper are optimal or almost optimal.