Constacyclic and quasi-twisted codes over $\mathbb{Z}_q [u] / \langle u^2 - 1 \rangle$ and new $\mathbb{Z}_4$-linear codes

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Constacyclic and quasi-twisted codes over \(\mathbb{Z}_q [u] / \langle u^2 - 1 \rangle\) and new \(\mathbb{Z}_4\)-linear codes