We consider quantum MDS (QMDS) codes for quantum systems of dimension q with lengths up to q2 + 2 and minimum distances up to q + 1. We show how starting from QMDS codes of length q2 + 1 based on cyclic and constacyclic codes, new QMDS codes can be obtained by shortening. We provide numerical evidence for our conjecture that almost all admissible lengths, from a lower bound n0(q,d) on, are achievable by shortening. Some additional codes that \ufb01ll gaps in the list of achievable lengths are presented as well along with a construction of a family of QMDS codes of length q2 +2, where q = 2m, that appears to be new.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider quantum MDS (QMDS) codes for quantum systems of dimension q with lengths up to q2 + 2 and minimum distances up to q + 1. We show how starting from QMDS codes of length q2 + 1 based on cyclic and constacyclic codes, new QMDS codes can be obtained by shortening. We provide […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"IEEE - Institute of Electrical and Electronics Engineers","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT'15), Hong Kong","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"1104\u20131108","msr_page_range_start":"1104","msr_page_range_end":"1108","msr_series":"","msr_volume":"","msr_copyright":"\u00a9 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting\/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.","msr_conference_name":"Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT'15), Hong Kong","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"M. Grassl, M. 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