Revisiting the Factorization of xⁿ+1 over Finite Fields

2020/09/21 by Arunwan Boripan, Boripan, Arunwan, Somphong Jitman +1
Computer Science · #11T60 #11T71 #12Y05 #Cellular Automata and Applications #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2009.09601

openalex publication_date 2020/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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