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

Year 2017, Volume: 4 Issue: 1, 37 - 47, 11.01.2017

Olav Geil Stefano Martin Umberto Martínez-peñas Diego Ruano

https://doi.org/10.13069/jacodesmath.34390

Cited By: 1

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

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