Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are closely connected to several areas in mathematics. There are a few fundamental ways of constructing all cyclic codes over finite fields, including the generator matrix approach, the generator polynomial approach, the generating idempotent approach, and the $q$-polynomial 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 the past decade in this direction.

翻译：有限域上的循环码因其具有高效的编码与解码算法，被广泛应用于数据存储系统、通信系统及消费电子产品中。在理论层面，循环码亦具有重要意义，因其与数学的多个领域紧密关联。构造有限域上所有循环码存在若干基本方法，包括生成矩阵法、生成多项式法、生成幂等元法以及$q$-多项式法。另一种方法是序列构造法，该方法在过去十年间得到了深入研究。本文旨在综述过去十年间该方向的研究进展。