Cyclic codes as a subclass of linear codes have practical applications in communication systems, consumer electronics, and data storage systems due to their efficient encoding and decoding algorithms. The objective of this paper is to construct some cyclic codes by the sequence approach. More precisely, we determine the dimension and the generator polynomials of three classes of q-ary cyclic codes defined by some sequences with explicit polynomials over \(\mathbb{F}_{q}m\). The minimum distance of such cyclic codes is also discussed. Some of these codes are optimal according to code tables. Moreover, the third class of cyclic codes provides some answers for Open Problem 3 proposed by Ding and Zhou in [1].

中文翻译：

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$$ \ mathbb {F} _ {q} m $$ F q m上来自显式单项式的一些q进制循环码

循环码作为线性码的子类，由于其有效的编码和解码算法，因此在通信系统，消费类电子产品和数据存储系统中具有实际应用。本文的目的是通过序列方法构造一些​​循环码。更准确地说，我们确定由\（\ mathbb {F} _ {q} m \）上具有显式多项式的某些序列定义的三类q进制循环码的维数和生成多项式。还讨论了这种循环码的最小距离。根据代码表，其中一些代码是最佳的。此外，第三类循环码为丁和周在[1]中提出的开放问题3提供了一些答案。