dc.contributor.author | Danielsen, Lars Eirik | eng |
dc.date.accessioned | 2013-04-30T11:03:05Z | |
dc.date.available | 2013-04-30T11:03:05Z | |
dc.date.issued | 2012-08 | eng |
dc.Published | IEEE Transactions on Information Theory 58(8): 5500-5511 | eng |
dc.identifier.issn | 0018-9448 | en_US |
dc.identifier.uri | https://hdl.handle.net/1956/6541 | |
dc.description.abstract | Additive 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.iso | eng | eng |
dc.publisher | Institute of Electrical and Electronics Engineers | en_US |
dc.title | On the Classification of Hermitian Self-Dual Additive Codes over GF(9) | en_US |
dc.type | Peer reviewed | |
dc.type | Journal article | |
dc.description.version | acceptedVersion | en_US |
dc.rights.holder | Copyright 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.doi | https://doi.org/10.1109/tit.2012.2196255 | |
dc.identifier.cristin | 937419 | |
dc.source.journal | IEEE Transactions on Information Theory | |
dc.source.40 | 58 | |
dc.source.14 | 8 | |
dc.source.pagenumber | 5500-5511 | |