Paper Info
Title
Decoding a Class of Affine Variety Codes with Fast DFT
Abstract
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.
Year
Venue
Keywords
2012
ISITA
Hermitian matrices,Reed-Solomon codes,affine transforms,decoding,discrete Fourier transforms,error correction codes,Berlekamp-Massey-Sakata algorithm,Grobner basis,Hermitian code,Reed-Solomon codes,affine variety codes,erasure-and-error decoding,error correcting pairs,error-value calculations,fast DFT,fast discrete Fourier transforms,linear equations,linear recurrence relations,multidimensional DFT,systematic encoding
DocType
Volume
Citations 
Journal
abs/1210.0083
1
PageRank 
References 
Authors
0.35
0
1
Name
Order
Citations
PageRank
Hajime Matsui1188.14