Transitive and Self-dual Codes Attaining the Tsfasman-Vladut-Zink Bound

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dc.creatorStichtenoth, Henning
dc.date2005-06-14
dc.date.accessioned2026-07-07T05:20:44Z
dc.date.available2026-07-07T05:20:44Z
dc.descriptionWe introduce - as a generalization of cyclic codes - the notion of transitive codes, and we show that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vladut-Zink bound over F_q, for all aquares q=l^2. We also show that self-orthogonal and self-dual codes attain the Tsfasman-Vladut-Zink bound, thus improving previous results about self-dual codes attaining the Gilbert-Varshamov bound. The main tool is a new asymptotically optimal tower (E_n) of function fields over F_q where all extensions E_n/E_0 are Galois.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0506264
dc.identifierhttp://arxiv.org/abs/math/0506264
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75484
dc.subjectAlgebraic Geometry
dc.subject14H25; 11R58
dc.titleTransitive and Self-dual Codes Attaining the Tsfasman-Vladut-Zink Bound
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