Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound

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Stichtenoth, Henning (2006) Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound. IEEE Transactions On Information Theory, 52 (5). pp. 2218-2224. ISSN 0018-9448

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Official URL: http://dx.doi.org/10.1109/TIT.2006.872986


A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and it is shown that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vladut-Zink bound over F-q, for all squares q = l(2). It is also shown 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-0 subset of E-1 subset of E-2 subset of center dot center dot center dot of function fields over F-q (with q = l(2)), where all extensions E-n/E-0 are Galois.

Item Type:Article
Uncontrolled Keywords:asymptotically good codes; cyclic codes; self-dual codes; towers of function fields; transitive codes; Tsfasman-Vladut-Zink bound
Subjects:T Technology > TK Electrical engineering. Electronics Nuclear engineering
ID Code:211
Deposited By:Henning Stichtenoth
Deposited On:20 Dec 2006 02:00
Last Modified:17 Sep 2019 13:47

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