naa a22 4500 510782612 CHVBK 20180411083252.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0126-9 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0126-9 Randriambololona Hugues École nationale supérieure des télécommunications ("Telecom ParisTech”) & LTCI CNRS UMR 5141, 46 rue Barrault, 75634, Paris cedex 13, France aut (2, 1)-Separating systems beyond the probabilistic bound [Elektronische Daten] [Hugues Randriambololona] Building on previous results of Xing, we give new lower bounds on the rate of linear intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry (although nothing beyond the basic theory of linear systems on curves). Then, using these new bounds within a concatenation argument, we construct binary (2,1)-separating systems of asymptotic rate exceeding the one given by the probabilistic method, which was the best lower bound available up to now. This answers (negatively) the question of whether this probabilistic bound was exact, which has remained open for more than 30 years. Hebrew University Magnes Press, 2013 Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/1(2013-06-01), 171-186 0021-2172 195:1<171 2013 195 11856 https://doi.org/10.1007/s11856-012-0126-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0126-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Randriambololona Hugues École nationale supérieure des télécommunications ("Telecom ParisTech”) & LTCI CNRS UMR 5141, 46 rue Barrault, 75634, Paris cedex 13, France aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/1(2013-06-01), 171-186 0021-2172 195:1<171 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer