Tsfasman-Vladut-Zink (TVZ) code
Member of a family of residue AG codes where \(\cal X\) is either a reduction of a Shimura curve or an elliptic curve of varying genus.
TVZ codes exceed the asymptotic Gilbert-Varshamov (GV) bound  (see also Ref. ). Roughly speaking, this breakthrough result implies that AG codes can outperform random codes. Such families of codes are optimal.
- M. A. Tsfasman, S. G. Vlădutx, and T. Zink, “Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound”, Mathematische Nachrichten 109, 21 (1982). DOI
- Y. Ihara. "Some remarks on the number of rational points of algebraic curves over finite fields." J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28:721-724 (1982),1981.
Zoo code information
“Tsfasman-Vladut-Zink (TVZ) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/shimura