Selected Article

Title

Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower

Description

Asymptotically good sequences of ramp secret sharing schemes were given in [5] by using one-pointalgebraic geometric codes defined from asymptotically good towers of function fields. Their securityis given by the relative generalized Hamming weights of the corresponding codes. In this paper wedemonstrate how to obtain refined information on the RGHWs when the codimension of the codes issmall. For general codimension, we give an improved estimate for the highest RGHW.