caa a22 4500 477040772 CHVBK 20180405111317.0 cr unu---uuuuu 170330e19961001xx s 000 0 eng 10.1023/A:1027358511882 doi (NATIONALLICENCE)springer-10.1023/A:1027358511882 Walker Judy Department of Mathematics, University of 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 statesthat for every linear [n, k] MDS code over $${\mathbb{F}}$$ q, if 1 <k < q, then n ≤ q+1,except when q is even and k=3 or k=q-1,in which cases n ≤ q +2. Recently, there has beenan attempt to prove the conjecture in the case of algebraic-geometriccodes. The method until now has been to reduce the conjectureto a statement about the arithmetic of the jacobian of the curve,and the conjecture has been successfully proven in this way forelliptic and hyperelliptic curves. We present a new approachto the problem, which depends on the geometry of the curve afteran appropriate embedding. Using algebraic-geometric methods,we then prove the conjecture through this approach in the caseof elliptic curves. In the process, we prove a new result aboutthe maximum number of points in an arc which lies on an ellipticcurve. Kluwer Academic Publishers, 1996 Algebraic-geometric codes nationallicence MDS codes nationallicence elliptic curves nationallicence Designs, Codes and Cryptography Kluwer Academic Publishers 9/1(1996-10-01), 115-120 0925-1022 9:1<115 1996 9 10623 https://doi.org/10.1023/A:1027358511882 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1027358511882 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Walker Judy Department of Mathematics, University of Illinois, 61801, Urbana, IL aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 9/1(1996-10-01), 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