Relative generalized Hamming weights of one-point algebraic geometric codes

Abstract

Producción CientíficaSecurity of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper, we elaborate on the implication of these parameters and devise a method to estimate their value for general one-point algebraic geometric codes. As it is demonstrated, for Hermitian codes, our bound is often tight. Furthermore, for these codes, the relative generalized Hamming weights are often much larger than the corresponding generalized Hamming weights.This research is supported by the Danish National Research Foundation, the National Natural Science Foundation of China (Grant No. 11061130539 - the Danish-Chinese Center for Applications of Algebraic Geometry in Coding Theory and Cryptography), Japan Society for the Promotion of Science (Grant Nos. 23246071 and 26289116), the Danish Council for Independent Research (Grant No. DFF--4002-00367), the Spanish MINECO (Grant No. MTM2012-36917-C03-03), National Basic Research Program of China (Grant No. 2013CB338004), and National Natural Science Foundation of China (Grant No. 61271222)