Revisiting the factorization of \(x^n+1\) over finite fields with applications (Q1983385)

Summary: 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.