  One central theme in quantum error-correction is to construct quantum codes
that have a large minimum distance. In this paper, we first present a
construction of classical codes based on certain class of polynomials. Through
these classical codes, we are able to obtain some new quantum codes. It turns
out that some of quantum codes exhibited here have better parameters than the
ones available in the literature. Meanwhile, we give a new class of quantum
synchronizable codes with highest possible tolerance against misalignment from
duadic codes.
