Abstract:
Results of recent investigations at the juncture of coding theory, the theory of computability, and algebraic geometry over finite fields are presented. The basic problems of the asymptotic theory of codes and Goppa's construction of codes on the basis of algebraic curves are presented, and a detailed algorithmic analysis is given of the codes arising on the modular curves of elliptic modules of V. G. Drinfel'd.
Citation:
S. G. Vlăduţ, Yu. I. Manin, “Linear codes and modular curves”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 25, VINITI, Moscow, 1984, 209–257; J. Soviet Math., 30:6 (1985), 2611–2643
\Bibitem{VlaMan84}
\by S.~G.~Vl{\u a}du\c t, Yu.~I.~Manin
\paper Linear codes and modular curves
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1984
\vol 25
\pages 209--257
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd77}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=770943}
\zmath{https://zbmath.org/?q=an:0629.94013}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 30
\issue 6
\pages 2611--2643
\crossref{https://doi.org/10.1007/BF02249124}
Linking options:
https://www.mathnet.ru/eng/intd77
https://www.mathnet.ru/eng/intd/v25/p209
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