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

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Olav Geil¹  Stefano Martin¹  Umberto Martínez-Peñas¹  Diego Ruano¹ 

[1] Department of Mathematical Sciences, Aalborg University

关键词: Algebraic geometric codes;    Asymptotically good ramp secret sharing schemes;    Generalized Hamming weights;    Relative generalized Hamming weights;    Secret sharing;   

DOI  :  10.13069/jacodesmath.34390

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

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.

【 授权许可】

CC BY