Support-Primitive Decomposition of Constacyclic Codes over Finite Fields: Coefficients-Based and Roots-Based Descriptions

Let $\mathcal C=(f)$ be a $λ$-constacyclic code over $\mathbb F_q$, where $f(X)$ is a monic factor of $X^N-λ$ with nonzero constant term. We introduce the support period $\operatorname{sp}(f)$ of $f(X)$, and define its support-primitive core $f_{\mathrm{sp}}(X)$ as the unique support-primitive polyn