Author/Authors :
geil, olav aalborg university - department of mathematical sciences, Aalborg, Denmark , martin, stefano aalborg university - department of mathematical sciences, Aalborg, Denmark , martínez-peñas, umberto aalborg university - department of mathematical sciences, Aalborg, Denmark , ruano, diego aalborg university - department of mathematical sciences, Aalborg, Denmark
Abstract :
Asymptotically good sequences of ramp secret sharing schemes were given in [5] by using one-point algebraic geometric codes defined from asymptotically good towers of function fields. Their security is given by the relative generalized Hamming weights of the corresponding codes. In this paper we demonstrate how to obtain refined information on the RGHWs when the codimension of the codes is small. For general codimension, we give an improved estimate for the highest RGHW.
Keywords :
Algebraic geometric codes , Asymptotically good ramp secret sharing schemes , Generalized Hamming weights , Relative generalized Hamming weights , Secret sharing
