Entanglement-Assisted Quantum Codes from a Class of Unitary Matrices

We craft a special class of unitary matrices over
$\mathbb{F}q^{2}$
to generate classical linear codes whose Hermitian hulls have dimensions that we can design. We then use the codes as classical ingredients in the construction of good entanglement-assisted quantum codes. Over finite fields of characteristic 2, we propose two explicit constructions. To highlight their efficacy, we list excellent qubit codes whose parameters are either new or strictly better than comparable best-known codes in the literature.