Transitive and Self-dual Codes Attaining the Tsfasman-Vladut-Zink Bound
Abstract
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 Fq, for all aquares q=l2. 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 (En) of function fields over Fq where all extensions En/E0 are Galois.
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