2012/09/29 by Hajime Matsui, Matsui, Hajime
Computer Science · Engineering · Mathematics · #Algebraic Geometry (math.AG) #Cellular Automata and Applications #Coding theory and cryptography #Commutative Algebra (math.AC) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.DM #cs.IT #graph theory and CDMA systems #math.AC #math.AG #math.IT
paper · pdf · doi:10.48550/arxiv.1210.0083
5 pages, 1 figure, to be presented at 2012 International Symposium on Information Theory and its Applications (ISITA2012)
arxiv created 2012/09/29 · openalex publication_date 2012/09/29 · arxiv updated 2012/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine variety codes is proposed. Our procedure is achieved by multidimensional DFT and linear recurrence relations from Grobner basis and is applied to erasure-and-error decoding and systematic encoding. The computational complexity of error-value calculations in our algorithm improves that in solving systems of linear equations from error correcting pairs in many cases. A motivating example of our algorithm in case of a Reed-Solomon code and a numerical example of our algorithm in case of a Hermitian code are also described.