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

Volume

60

Issue

10

fYear

2014

fDate

Oct. 2014

Firstpage

5938

Lastpage

5949

Abstract

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 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; cryptography; Hermitian codes; cryptographic method; general one-point algebraic geometric codes; linear ramp secret sharing schemes; relative generalized Hamming weights; Cryptography; Electronic mail; Hamming weight; Linear codes; Materials; Random variables; Vectors; Feng-Rao bound; Hermitian code; Linear code; one-point algebraic geometric code; relative dimension/length profile; relative generalized Hamming weight; secret sharing; wiretap channel of type II;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2014.2345375

Filename

6871379