We study quadratic residue circulant matrices and consider the Hermitian hulls of linear codes constructed from such matrices. Conditions for which the matrices are unitary are characterized. They can then serve as ingredients to produce infinitely many linear codes over \(\mathbb {F}_{q^2}\) with flexible Hermitian hull dimensions. We devise an approach to explicitly determine the Hermitian hull dimensions of linear codes with varied lengths. We also consider linear codes over \(\mathbb {F}_{q^2}\) generated by noncirculant unitary matrices, leading to codes with arbitrary Hermitian hull dimensions. In this respect, we also establish a lower bound on the respective minimum distances of the constructed codes over \(\mathbb {F}_{q^2}\) for \(q=2^m\) and \(q=3^m\) , with m being a positive integer. As an application, we derive the parameters of q-ary entanglement-assisted quantum error-correcting codes (EAQECCs) based on the well-known Hermitian construction route. Over small values of \(q \in \{2,3\}\) , we make meaningful parameter comparisons with currently best-known EAQECCs on record.
