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On the decoding of algebraicgeometric codes
 IEEE TRANS. INFORM. THEORY
, 1995
"... This paper provides a survey of the existing literature on the decoding of algebraicgeometric codes. Definitions, theorems and cross references will be given. We show what has been done, discuss what still has to be done and pose some open problems. The following subjects are examined in a more or ..."
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Cited by 31 (6 self)
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This paper provides a survey of the existing literature on the decoding of algebraicgeometric codes. Definitions, theorems and cross references will be given. We show what has been done, discuss what still has to be done and pose some open problems. The following subjects are examined in a more
Efficient RootFinding Algorithm with Application to List Decoding of AlgebraicGeometric Codes
 IEEE Trans. Inform. Theory
, 2001
"... A list decoding for an errorcorrecting code is a decoding algorithm that generates a list of codewords within a Hamming distance t from the received vector, where t can be greater than the errorcorrection bound. In [18], a listdecoding procedure for ReedSolomon codes [19] was generalized to alg ..."
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Cited by 16 (4 self)
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to algebraicgeometric codes. A recent work [8] gives improved list decodings for ReedSolomon codes and algebraicgeometric codes that work for all rates and have many applications. However, these listdecoding algorithms are rather complicated. In [17], Roth and Ruckenstein proposed an e#cient implementation
Generalized BerlekampMassey Decoding of AlgebraicGeometric Codes up to Half the FengRao Bound
"... AbstiuctWe treat a general class of algebraicgeometric codes and show how to decode these up to half the FengRao bound, using an extension and modification of the Sakata algorithm. The Sakata algorithm is a generalization to N dimensions of the classical BerlekampMassey algorithm. E Index Terms ..."
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AbstiuctWe treat a general class of algebraicgeometric codes and show how to decode these up to half the FengRao bound, using an extension and modification of the Sakata algorithm. The Sakata algorithm is a generalization to N dimensions of the classical BerlekampMassey algorithm. E Index TermsDecoding
Inversefree Berlekamp–Massey–Sakata Algorithm and Small Decoders for AlgebraicGeometric Codes
, 2007
"... This paper proposes a novel algorithm for finding errorlocators of algebraicgeometric codes that can eliminate the divisioncalculations of finite fields from the Berlekamp– Massey–Sakata algorithm. This inversefree algorithm provides full performance in correcting a certain class of errors, gen ..."
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This paper proposes a novel algorithm for finding errorlocators of algebraicgeometric codes that can eliminate the divisioncalculations of finite fields from the Berlekamp– Massey–Sakata algorithm. This inversefree algorithm provides full performance in correcting a certain class of errors
Reflections on the "Decoding of AlgebraicGeometric Codes up to the Designed Minimum Distance"
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List Decoding of AlgebraicGeometric Codes
 IEEE Trans. on Information Theory
, 1999
"... We generalize Sudan's results for ReedSolomon codes to the class of algebraicgeometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional errorcorrection bound (d\Gamma1)=2, d being the minimumdistance of the code. Our main alg ..."
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Cited by 45 (3 self)
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We generalize Sudan's results for ReedSolomon codes to the class of algebraicgeometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional errorcorrection bound (d\Gamma1)=2, d being the minimumdistance of the code. Our main
On the efficient decoding of . . .
 APPEARED IN EUROCODE 92, (P.CAMION, P. CHARPIN AND S. HARARI EDS.)
, 1993
"... This talk is intended to give a survey on the existing literature on the decoding of algebraicgeometric codes. Although the motivation originally was to find an efficient decoding algorithm for algebraicgeometric codes, the latest results give algorithms which can be explained purely in terms of l ..."
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This talk is intended to give a survey on the existing literature on the decoding of algebraicgeometric codes. Although the motivation originally was to find an efficient decoding algorithm for algebraicgeometric codes, the latest results give algorithms which can be explained purely in terms
List Decoding of AlgebraicGeometric Codes
, 2001
"... We generalize the list decoding algorithm for onepoint (strongly) algebraicgeometric codes by Guruswami and Sudan to all algebraicgeometric codes. Moreover, our algorithm works for a generalized Hamming distance with real weight coefficients rather than integer weight coefficients. This is more s ..."
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Cited by 5 (0 self)
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We generalize the list decoding algorithm for onepoint (strongly) algebraicgeometric codes by Guruswami and Sudan to all algebraicgeometric codes. Moreover, our algorithm works for a generalized Hamming distance with real weight coefficients rather than integer weight coefficients. This is more
On Representations of AlgebraicGeometric Codes
 IEEE TRANSACTIONS ON INFORMATION THEORY
"... We show that all algebraicgeometric codes possess a succinct representation that allows for the list decoding algorithms of [9, 6] to run in polynomial time. We do this by presenting a rootfinding algorithm for univariate polynomials over function fields when their coefficients lie in finitedi ..."
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Cited by 6 (4 self)
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We show that all algebraicgeometric codes possess a succinct representation that allows for the list decoding algorithms of [9, 6] to run in polynomial time. We do this by presenting a rootfinding algorithm for univariate polynomials over function fields when their coefficients lie in finite
Results 1  10
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