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

By Henning Stichtenoth. 2005

56 citations recorded by the source corpus.

We 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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/25e2cec1b446d367ba1e652fdbc6643077af0153

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Citations in the corpus

• Handbook of Finite Fields (2013, background): “), where F̂n is the Galois closure of Fn/F0, is also asymptotically good, see [16, 39].”