Relative Generalized Hamming Weights of One-Point Algebraic Geometric Codes11The paper is registered to the ORCID of Olav Geil. For more details please visit Ryutaroh Matsumoto: http: //orcid.org/0000-0002-5085-8879 or Diego Ruano: http: //orcid.rg/0000-0001-7304-0087

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes [26, 24]. In this paper we elaborate on the implication of these parameters and we 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.