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dc.contributor.authorDanielsen, Lars Eirikeng
dc.date.accessioned2013-04-30T11:03:05Z
dc.date.available2013-04-30T11:03:05Z
dc.date.issued2012-08eng
dc.PublishedIEEE Transactions on Information Theory 58(8): 5500-5511eng
dc.identifier.issn0018-9448en_US
dc.identifier.urihttps://hdl.handle.net/1956/6541
dc.description.abstractAdditive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. However, these codes have so far received far less interest from coding theorists than self-dual additive codes over GF(4), which correspond to binary quantum codes. Self-dual additive codes over GF(9) have been classified up to length 8, and in this paper we extend the complete classification to codes of length 9 and 10. The classification is obtained by using a new algorithm that combines two graph representations of self-dual additive codes. The search space is first reduced by the fact that every code can be mapped to a weighted graph, and a different graph is then introduced that transforms the problem of code equivalence into a problem of graph isomorphism. By an extension technique, we are able to classify all optimal codes of length 11 and 12. There are 56 005 876 (11; 311; 5) codes and 6493 (12; 312; 6) codes. We also find the smallest codes with trivial automorphism group.en_US
dc.language.isoengeng
dc.publisherInstitute of Electrical and Electronics Engineersen_US
dc.titleOn the Classification of Hermitian Self-Dual Additive Codes over GF(9)en_US
dc.typePeer reviewed
dc.typeJournal article
dc.description.versionacceptedVersionen_US
dc.rights.holderCopyright 2012 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.en_US
dc.identifier.doihttps://doi.org/10.1109/tit.2012.2196255
dc.identifier.cristin937419
dc.source.journalIEEE Transactions on Information Theory
dc.source.4058
dc.source.148
dc.source.pagenumber5500-5511


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