2014/03/31 by Olav Geil, Stefano Martin, Ryutaroh Matsumoto +2
Computer Science · Engineering · Mathematics · #Algorithm #Block code #Coding theory and cryptography #Combinatorics #Cryptography and Data Security #Decoding methods #Discrete mathematics #Hamming bound #Hamming code #Hamming distance #Hamming graph #Hamming weight #Hamming(7,4) #Hermitian matrix #Linear code #Mathematics #Point (geometry) #Pure mathematics #cs.IT #graph theory and CDMA systems #math.AG #math.IT
paper · pdf · doi:10.1109/tit.2014.2345375
published as IEEE Transactions on Information Theory, vol. 60, no. 10, pp. 5938-5949, October 2014
arxiv created 2014/07/24 · openalex publication_date 2014/08/05 · arxiv updated 2015/02/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.