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

2005/06/14 by Henning Stichtenoth, Stichtenoth, Henning · 4 citations
Computer Science · Mathematics · #11R58 #14H25 #Algebraic Geometry (math.AG) #Cellular Automata and Applications #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #math.AG #msc:11R58 #msc:14H25

paper · pdf · doi:10.48550/arxiv.math/0506264

17 pages

arxiv created 2005/06/14 · openalex publication_date 2005/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 F_q, 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 (E_n) of function fields over F_q where all extensions E_n/E₀ are Galois.

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