  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. There are several approaches to
constructing all cyclic codes over finite fields, including the generator
matrix approach, the generator polynomial approach, and the generating
idempotent approach. Another one is a sequence approach, which has been
intensively investigated in the past decade. The objective of this paper is to
survey the progress in this direction in the past decade. Many open problems
are also presented in this paper.
