Title :
Relative generalized Hamming weights of one-point algebraic geometric codes
Author :
Geil, Olav ; Martin, Sebastien ; Matsumoto, R. ; Ruano, Diego ; Yuan Luo
Author_Institution :
Dept. of Math. Sci., Aalborg Univ., Aalborg, Denmark
Abstract :
Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes [23], [22]. 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.
Keywords :
Hamming codes; algebraic geometric codes; security of data; Hermitian codes; general one-point algebraic geometric codes; linear ramp secret sharing schemes security; relative generalized Hamming weights; Cryptography; Galois fields; Geometry; Hamming weight; Linear codes; Vectors;
Conference_Titel :
Information Theory Workshop (ITW), 2014 IEEE
Conference_Location :
Hobart, TAS
DOI :
10.1109/ITW.2014.6970808