Revisiting the Factorization of xn+1 over Finite Fields with Applications - Arunwan Boripan; Somphong Jitman (Journal of Mathematics)
The polynomial xn+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 xn+1 over finite fields is given as well as its applications. Explicit and recursive methods for factorizing xn+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.