Journal ArticleDOI
On a decoding algorithm for codes on maximal curves
TLDR
A decoding algorithm for algebraic geometric codes that was given by A.N. Skorobogatov and S.G. Vladut is considered and the author gives a modified algorithm, with improved performance, which he obtains by applying the above algorithm a number of times in parallel.Abstract:
A decoding algorithm for algebraic geometric codes that was given by A.N. Skorobogatov and S.G. Vladut (preprint, Inst. Problems of Information Transmission, 1988) is considered. The author gives a modified algorithm, with improved performance, which he obtains by applying the above algorithm a number of times in parallel. He proves the existence of the decoding algorithm on maximal curves by showing the existence of certain divisors. However, he has so far been unable to give an efficient procedure of finding these divisors. >read more
Citations
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Book
Algebraic Geometric Codes: Basic Notions
TL;DR: The theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics, is studied in this paper, where the authors constantly look for interpretations that connect coding theory to algebraic geometry and number theory.
Journal ArticleDOI
Algebraic-geometry codes
TL;DR: Elements of the theory of algebraic curves, at a level sufficient to understand the code constructions and decoding algorithms, are introduced.
Book
List Decoding of Error-Correcting Codes
Venkatesan Guruswami,Madhu Sudan +1 more
TL;DR: This thesis presents a detailed investigation of list decoding, and proves its potential, feasibility, and importance as a combinatorial and algorithmic concept and presents the first polynomial time algorithm to decode Reed-Solomon codes beyond d/2 errors for every value of the rate.
Journal ArticleDOI
Decoding algebraic-geometric codes up to the designed minimum distance
Gui-Liang Feng,T.R.N. Rao +1 more
TL;DR: This decoding procedure is a generalization of Peterson's decoding procedure for the BCH codes and can be used to correct any ((d*-1)/2) or fewer errors with complexity O(n/sup 3/), where d* is the designed minimum distance of the algebraic-geometric code and n is the codelength.
Journal ArticleDOI
On the decoding of algebraic-geometric codes
T. Hoholdt,Ruud Pellikaan +1 more
TL;DR: This paper provides a survey of the existing literature on the decoding of algebraic-geometric codes and shows what has been done, discusses what still has to be done, and poses some open problems.
References
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Projective geometries over finite fields
TL;DR: The first properties of the plane can be found in this article, where the authors define the following properties: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. Ovals 9. Arithmetic of arcs of degree two 10. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes 15.
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Introduction to the theory of algebraic functions of one variable
TL;DR: In this paper, the authors present an approach to algebraic geometry of curves treated as the theory of algebraic functions on the curve, which allows the author to consider curves over an arbitrary ground field.
Journal ArticleDOI
Algebraico-geometric codes
TL;DR: An algebraico-geometric approach to coding theory is developed and linear series on an algebraic curve are used for the construction and analysis of error-correcting codes.
Journal ArticleDOI
Construction and decoding of a class of algebraic geometry codes
TL;DR: A decoding algorithm is constructed which turns out to be a generalization of the Peterson algorithm for decoding BCH decoder codes.