On the Classification of All Self-Dual Additive Codes over GF(4) of Length up to 12

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dc.creatorDanielsen, Lars Eirik
dc.creatorParker, Matthew G.
dc.date2005-04-25
dc.date2006-02-17
dc.date.accessioned2026-07-07T08:53:21Z
dc.date.available2026-07-07T08:53:21Z
dc.descriptionWe consider additive codes over GF(4) that are self-dual with respect to the Hermitian trace inner product. Such codes have a well-known interpretation as quantum codes and correspond to isotropic systems. It has also been shown that these codes can be represented as graphs, and that two codes are equivalent if and only if the corresponding graphs are equivalent with respect to local complementation and graph isomorphism. We use these facts to classify all codes of length up to 12, where previously only all codes of length up to 9 were known. We also classify all extremal Type II codes of length 14. Finally, we find that the smallest Type I and Type II codes with trivial automorphism group have length 9 and 12, respectively.
dc.description18 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0504522
dc.identifierhttp://arxiv.org/abs/math/0504522
dc.identifierJournal of Combinatorial Theory, Series A 113(7), pp. 1351-1367, 2006
dc.identifierdoi:10.1016/j.jcta.2005.12.004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145592
dc.subjectCombinatorics
dc.subjectInformation Theory
dc.subject94B60 (Primary) 05C90 (Secondary)
dc.titleOn the Classification of All Self-Dual Additive Codes over GF(4) of Length up to 12
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