论文标题
在有限字段上重新审查$ x^n+1 $的分解
Revisiting the Factorization of $x^n+1$ over Finite Fields
论文作者
论文摘要
有限字段上的多项式$ x^n+1 $由于其在有限领域的负面代码方面的应用而引起了人们的关注。在本文中，对有限领域的$ x^n+1 $分解的严格处理及其应用。在有限字段上分解$ x^n+1 $的显式和递归方法与枚举公式一起提供。作为应用程序，一些否定码的家庭以更清晰，更简单的形式重新审视。
The polynomial $x^n+1$ 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 $x^n+1$ over finite fields is given as well as its applications. Explicit and recursive methods for factorizing $x^n+1$ 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.
