  Near MDS (NMDS) codes are closely related to interesting objects in finite
geometry and have nice applications in combinatorics and cryptography. But
there are many unsolved problems about construction of NMDS codes. In this
paper, by using symmetrical orthogonal arrays (OAs), we construct a lot of
NMDS, $m$-MDS and almost extremal NMDS codes. We establish a relation between
asymmetrical OAs and quantum error correcting codes (QECCs) over mixed
alphabets. Since quantum maximum distance separable (QMDS) codes over mixed
alphabets with the dimension equal to one have not been found in all the
literature so far, the definition of a near quantum maximum distance separable
(NQMDS) code over mixed alphabets is proposed. By using asymmetrical OAs, we
obtain many such codes.
