Negacyclic code ($C◃{\mathbb{F}}_q[X]/(X^n+1)$)

A linear code is negacyclic if $(c_0,\dots ,c_{n-1})$ being a codeword implies that $(-c_{n-1},c_0,\dots ,c_{n-2})$ is a codeword. Polynomial identification makes it an ideal modulo $X^n+1$. For odd $n$, the substitution $X\mapsto -X$ gives a monomial equivalence of linear codes between negacyclic and cyclic codes.