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Let <inline-formula> <tex-math notation="LaTeX">$F_{q}$ </tex-math></inline-formula> be a finite field of odd order <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>. Let <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> be a positive integer such that <inline-formula> <tex-math notation="LaTeX">$X^{2^{m}}+1$ </tex-math></inline-formula> factors completely into degree-one factors in <inline-formula> <tex-math notation="LaTeX">$F_{q^{2}}[X]$ </tex-math></inline-formula>. The polynomial generators of all negacyclic codes of length <inline-formula> <tex-math notation="LaTeX">$2^{m}p^{n}$ </tex-math></inline-formula> over <inline-formula> <tex-math notation="LaTeX">$F_{q}$ </tex-math></inline-formula> are obtained, where <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> is an odd prime coprime to <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>.

Negacyclic Codes of Length $2^mp^n$ Over Finite Fields