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Galindo, Carlos Geil, Olav Hernando, Fernando Ruano Benito, Diego 2018-09-24T11:46:46Z 2018-09-24T11:46:46Z 2018 IEEE Transactions on Information Theory. Volume 64, Issue 4, pages 2444-2459 (2018) http://uvadoc.uva.es/handle/10324/31722 Producción Científica Two new constructions of linear nested code pairs are given for which the codimension and the relative minimum distances of the codes and their duals are good. By this we mean that for any two out of the three parameters the third parameter of the constructed code pair is large. Such pairs of nested codes are indispensable for the determination of good linear ramp secret sharing schemes. They can also be used to ensure reliable communication over asymmetric quantum channels. The new constructions result from carefully applying the Feng-Rao bounds to a family of codes defined from multivariate polynomials and Cartesian product point sets. The Danish Council for Independent Research (Grant N. DFF–4002-00367) Ministerio de Economía, Industria y Competitividad (Projects MTM2015-65764-C3-2-P and MTM2015-69138-REDT) University Jaume I (Grant N. P1-1B2015-02) application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 International Improved constructions of nested code pairs info:eu-repo/semantics/article https://ieeexplore.ieee.org/document/8048519/ SI