Negacyclic code
= Negacyclic code
{title2=$C\triangleleft\mathbb F_q[X]/(X^n+1)$}
A <linear code> is negacyclic if $(c_0,\ldots,c_{n-1})$ being a <codeword> implies that $(-c_{n-1},c_0,\ldots,c_{n-2})$ 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>.