caa a22 4500 477041000 CHVBK 20180405111318.0 cr unu---uuuuu 170330e19960801xx s 000 0 eng 10.1007/BF00169780 doi (NATIONALLICENCE)springer-10.1007/BF00169780 Walker Judy Department of Mathematics, Universityof Illinois, 61801, Urbana, IL aut A new approach to the main conjecture on algebraic-geometric MDS Codes [Elektronische Daten] [Judy Walker] The Main Conjecture on MDS Codes states that for every linear [n, κ] MDS code over $$\mathbb{F}$$ q , if 1 < κ < q, then n ≤ q + 1, except when q is seven and κ = 3 or κ = q − 1, in which cases n ≤ q + 2. Recently, there has been an attempt to prove the conjecture in the case of algebraic-geometric codes. The method until now has been to reduce the conjecture to a statement about the arithmetic of the jacobian of the curve, and the conjecture has been successfully proven in this way for elliptic and hyperelliptic curves. We present a new approach to the problem, which depends on the geometry of the curve after an appropriate embedding. Using algebraic-geometric methods, we then prove the conjecture through this approach in the case of elliptic curves. In the process, we prove a new result about the maximum number of points in an arc which lies on an elliptic curve. Kluwer Academic Publishers, 1996 Algebraic-geometric codes nationallicence MDS codes nationallicence elliptic curves nationallicence Designs, Codes and Cryptography Kluwer Academic Publishers 9/1(1996-08-01), 115-120 0925-1022 9:1<115 1996 9 10623 https://doi.org/10.1007/BF00169780 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00169780 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Walker Judy Department of Mathematics, Universityof Illinois, 61801, Urbana, IL aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 9/1(1996-08-01), 115-120 0925-1022 9:1<115 1996 9 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 477040772 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer