The polynomial over finite fields has been of interest due to its applications in the study of negacyclic codes over finite fields. In this paper, a rigorous treatment of the factorization of over finite fields is given as well as its applications. Explicit and recursive methods for factorizing over finite fields are provided together with the enumeration formula. As applications, some families of negacyclic codes are revisited with more clear and simpler forms.

中文翻译：

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再次探讨超有限域的因式分解及其应用

多项式 由于其在有限域上的负循环码研究中的应用，使得有限域上的超码域引起了人们的兴趣。本文对因子分解进行了严格的处理给出了有限域及其应用。显式和递归分解方法提供了有限字段以及枚举公式。作为应用程序，以更清楚和更简单的形式重新介绍了一些负循环代码系列。