  Quantum error-correcting codes with good parameters can be constructed by
evaluating polynomials at the roots of the polynomial trace. In this paper, we
propose to evaluate polynomials at the roots of trace-depending polynomials
(given by a constant plus the trace of a polynomial) and show that this
procedure gives rise to stabilizer quantum error-correcting codes with a wider
range of lengths than in other papers involving roots of the trace and with
excellent parameters. Namely, we are able to provide new binary records and
non-binary codes improving the ones available in the literature.
