  Cyclic codes are a subclass of linear codes and have applications in consumer
electronics, data storage systems, and communication systems as they have
efficient encoding and decoding algorithms. In this paper, almost perfect
nonlinear functions and planar functions 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 are flexible. Many of the codes presented in this
paper are optimal or almost optimal in the sense that they meet some bound on
linear codes. Ten open problems regarding cyclic codes from highly nonlinear
functions are also presented.
