Relative generalized Hamming weights of one-point algebraic geometric codes

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 we devise a method to estimate their value for general one-point algebraic geometric codes. As...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2014-07
Main Authors: Geil, Olav, Martin, Stefano, Matsumoto, Ryutaroh, Ruano, Diego, Luo, Yuan
Format: Article
Language:English
Subjects:
Algebra
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1403.7985