  In this paper, we provide a framework for constructing entanglement-assisted
quantum error-correcting codes (EAQECCs) from classical additive codes over a
finite commutative local Frobenius ring $\mathcal{R}$. At the heart of the
framework, and this is one of the main technical contributions of our paper, is
a procedure to construct, for an additive code $\mathcal{C}$ over
$\mathcal{R}$, a generating set for $\mathcal{C}$ that is in standard form,
meaning that it consists purely of isotropic generators and hyperbolic pairs.
Moreover, when $\mathcal{R}$ is a Galois ring, we give an exact expression for
the minimum number of pairs of maximally entangled qudits required to construct
an EAQECC from an additive code over $\mathcal{R}$, which significantly extends
known results for EAQECCs over finite fields. We also demonstrate how adding
extra coordinates to an additive code can give us a certain degree of
flexibility in determining the parameters of the EAQECCs that result from our
construction.
