Relative Generalized Hamming Weights of One-Point Algebraic Geometric Codes
Olav Geil, Stefano Martin, Ryutaroh Matsumoto, Diego Ruano, Yuan Luo · IEEE Transactions on Information Theory · 2014
Security 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.