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20. Geometric coding 61
"... 21. Symbolic representation of geodesics via geometric code. 65 22. Arithmetic codings 68 23. Reduction theory conjecture 72 24. Symbolic representation of geodesics via arithmetic codes 75 25. Complexity of the geometric code 78 ..."
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21. Symbolic representation of geodesics via geometric code. 65 22. Arithmetic codings 68 23. Reduction theory conjecture 72 24. Symbolic representation of geodesics via arithmetic codes 75 25. Complexity of the geometric code 78
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
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
Algebraic Geometric Codes over Rings
, 2008
"... In this chapter, algebraic geometric codes over local, Artinian rings are defined and studied. Decoding algorithms for these codes are also presented. ..."
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In this chapter, algebraic geometric codes over local, Artinian rings are defined and studied. Decoding algorithms for these codes are also presented.
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
Universal Hashing and Geometric Codes
 DESIGNS, CODES AND CRYPTOGRAPHY
, 1997
"... We describe a new application of algebraic coding theory to universal hashing and authentication without secrecy. This permits to make use of the hitherto sharpest weapon of coding theory, the construction of codes from algebraic curves. We show in particular how codes derived from ArtinSchreier cu ..."
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Cited by 8 (0 self)
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We describe a new application of algebraic coding theory to universal hashing and authentication without secrecy. This permits to make use of the hitherto sharpest weapon of coding theory, the construction of codes from algebraic curves. We show in particular how codes derived from Artin
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
ALGEBRAIC GEOMETRIC CODES ON SURFACES by
"... Abstract. — We study errorcorrecting codes constructed from projective surfaces over finite fields using the generalized Goppa construction. We obtain bounds for the minimal distance of these codes by understanding how the zero sets of functions on a surface decompose into irreducible components. W ..."
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Cited by 3 (0 self)
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Abstract. — We study errorcorrecting codes constructed from projective surfaces over finite fields using the generalized Goppa construction. We obtain bounds for the minimal distance of these codes by understanding how the zero sets of functions on a surface decompose into irreducible components
NOTES ON ALGEBRAICGEOMETRIC CODES
"... Ideas from algebraic geometry became useful in coding theory after Goppa’s construction [8]. He had the beautiful idea of associating to a curve X defined over Fq, the finite field with q elements, a code C. This code, called AlgebraicGeometric (AG) code, is constructed from two divisors D and G on ..."
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Ideas from algebraic geometry became useful in coding theory after Goppa’s construction [8]. He had the beautiful idea of associating to a curve X defined over Fq, the finite field with q elements, a code C. This code, called AlgebraicGeometric (AG) code, is constructed from two divisors D and G
TWISTING GEOMETRIC CODES
"... Abstract. The aim of this paper is to explain how, starting from a Goppa code C(X,G, P1,..., Pn) and a cyclic covering pi: Y → X of degree m, one can twist the initial code to another one C(X,G + Dχ, P1,..., Pn), where Dχ is a nonprincipal degree 0 divisor on X associated to a character χ of Gal(Y/ ..."
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Abstract. The aim of this paper is to explain how, starting from a Goppa code C(X,G, P1,..., Pn) and a cyclic covering pi: Y → X of degree m, one can twist the initial code to another one C(X,G + Dχ, P1,..., Pn), where Dχ is a nonprincipal degree 0 divisor on X associated to a character χ of Gal
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