Sub-Quadratic Decoding of One-Point Hermitian Codes

We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power decodi...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 61; no. 6; pp. 3225 - 3240
Main Authors: Nielsen, Johan S. R., Beelen, Peter
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
AG codes
Algebra
Algorithms
Coding theory
Complexity theory
Computer Science
Decoding
Electronics
Guruswami-Sudan
Hermitian codes
Indexes
Information Theory
Interpolation
list decoding
Minimization
Polynomials
Power decoding
power decoding
Guruswami–Sudan
Hermitian codes
AG codes
list decoding
Power decoding
Guruswami-Sudan
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities.
Bibliography:SourceType-Scholarly Journals-1
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content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2424415