Fast decoding of codes from algebraic curves

The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves in an r-dimensional space can be decoded. He shows how Sakata's (1990) Berlekamp-Massey (1969) extension can be used to find an error lo...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 40; no. 1; pp. 223 - 229
Main Author: Dahl, C.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.1994
Institute of Electrical and Electronics Engineers
Subjects:
Applied sciences
Coding, codes
Costs
Decoding
Equations
Error correction
Exact sciences and technology
Geometry
Information, signal and communications theory
Polynomials
Signal and communications theory
Telecommunications and information theory
Algebraic code
BCH code
Decoding
Fast algorithm
Coding
ISSN:0018-9448
Online Access:Get full text
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Summary:The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves in an r-dimensional space can be decoded. He shows how Sakata's (1990) Berlekamp-Massey (1969) extension can be used to find an error locator polynomial, and also shows that the cost of doing this increases with the dimension of the space. Unfortunately, the error-correcting capability gets worse for codes from curves in higher dimensional spaces. For a specific curve, he determines the error values faster than by solving linear equations. The method is an extension of the transformation method known from cyclic codes.< >
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0018-9448
DOI:10.1109/18.272487