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(2, 1)-Separating systems beyond the probabilistic bound
Authors:Hugues Randriambololona
Institution:1. école nationale supérieure des télécommunications (“Telecom ParisTech”) & LTCI CNRS UMR 5141, 46 rue Barrault, 75634, Paris cedex 13, France
Abstract: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.
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