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Revisiting the Factorization of xn+1 over Finite Fields with Applications

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  • Arunwan Boripan
  • Somphong Jitman
  • Marco Fontana

Abstract

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.

Suggested Citation

  • Arunwan Boripan & Somphong Jitman & Marco Fontana, 2021. "Revisiting the Factorization of xn+1 over Finite Fields with Applications," Journal of Mathematics, Hindawi, vol. 2021, pages 1-10, January.
    • Handle: RePEc:hin:jjmath:6626422
    DOI: 10.1155/2021/6626422
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