Related papers: Near MDS and near quantum MDS codes via orthogonal arrays

Near MDS and near quantum MDS codes via orthogonal arrays

URL: http://arxiv.org/abs/2308.00406v1
Date: Tue, 1 Aug 2023 09:36:48 GMT
Title: Near MDS and near quantum MDS codes via orthogonal arrays
Authors: Shanqi Pang, Chaomeng Zhang, Mengqian Chen, Miaomiao Zhang
Abstract summary: 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.
Score: 3.5557219875516646
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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