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Coset bounds for algebraic geometric codes
, 2008
"... We develop new coset bounds for algebraic geometric codes. The bounds have a natural interpretation as an adversary threshold for algebraic geometric secret sharing schemes and lead to improved bounds for the minimum distance of an AG code. Our bounds improve both floor bounds and order bounds and p ..."
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Cited by 9 (2 self)
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We develop new coset bounds for algebraic geometric codes. The bounds have a natural interpretation as an adversary threshold for algebraic geometric secret sharing schemes and lead to improved bounds for the minimum distance of an AG code. Our bounds improve both floor bounds and order bounds
Algebraic Geometric Codes Over Rings
 Journal of Pure and Applied Algebra
, 1996
"... . The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980's. Recently, there has been an increased interest in the study of linear codes over finite rings. In this paper, we combine these two approaches ..."
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Cited by 5 (2 self)
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to coding theory by introducing the study of algebraic geometric codes over rings. In addition to defining these new codes, we prove several results about their properties. 1. Introduction Whenever data is transmitted across a channel, errors are likely to occur. The data is usually encoded as a string
RESIDUAL REPRESENTATION OF ALGEBRAICGEOMETRIC CODES
, 2001
"... Dedicated to T. Winiarski on the occasion of his sixtieth birthday. Abstract. In this paper residues and duality theory for curves are used to construct errorcorrecting codes and to find estimates for their parameters. Results of Goppa are extended to singular curves. In an attempt to find long cod ..."
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codes with good parameters, algebraicgeometric codes have been introduced by Goppa [4]. The construction is based on the (residual) evaluation of the space of sections of a line bundle on a nonsingular curve over a finite field at the points in the support of a given divisor. The explicit construction
Dictionary of protein secondary structure: pattern recognition of hydrogenbonded and geometrical features
 Biopolymers
, 1983
"... structure ..."
Minimum Weight and Dimension Formulas for Some Geometric Codes
, 1998
"... The geometric codes are the duals of the codes defined by the designs associated with finite geometries. The latter are generalized ReedMuller codes, but the geometric codes are, in general, not. We obtain values for the minimum weight of these codes in the binary case, using geometric construction ..."
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Cited by 1 (0 self)
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The geometric codes are the duals of the codes defined by the designs associated with finite geometries. The latter are generalized ReedMuller codes, but the geometric codes are, in general, not. We obtain values for the minimum weight of these codes in the binary case, using geometric
Algebraicgeometric codes from vector bundles and their decoding
, 803
"... Abstract — Algebraicgeometric codes can be constructed by evaluating a certain set of functions on a set of distinct rational points of an algebraic curve. The set of functions that are evaluated is the linear space of a given divisor or, equivalently, the set of section of a given line bundle. Usi ..."
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Abstract — Algebraicgeometric codes can be constructed by evaluating a certain set of functions on a set of distinct rational points of an algebraic curve. The set of functions that are evaluated is the linear space of a given divisor or, equivalently, the set of section of a given line bundle
On Representations of AlgebraicGeometric Codes for List Decoding
"... We show that all algebraicgeometric codes possess a succinct representation that allows for the list decoding algorithms of [15, 7] 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 ..."
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We show that all algebraicgeometric codes possess a succinct representation that allows for the list decoding algorithms of [15, 7] 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
Construction of a Class of AlgebraicGeometric Codes via Gröbner Bases
"... Abstract. In this paper, a class of algebraicgeometric codes from affine varieties are constructed. This construction is presented via Gröbner bases computation. In particular, we can get some algebraicgeometric codes more efficient than the current algebraic geometric codes. 1. ..."
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Abstract. In this paper, a class of algebraicgeometric codes from affine varieties are constructed. This construction is presented via Gröbner bases computation. In particular, we can get some algebraicgeometric codes more efficient than the current algebraic geometric codes. 1.
BOUNDING THE TRELLIS STATE COMPLEXITY OF ALGEBRAIC GEOMETRIC CODES
"... Abstract. Let C be an algebraic geometric code of dimension k and length n constructed on a curve X over Fq. Let s(C) be the state complexity of C and set w(C): = min{k, n−k}, the Wolf upper bound on s(C). We introduce a numerical function R that depends on the gonality sequence of X and show that s ..."
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Abstract. Let C be an algebraic geometric code of dimension k and length n constructed on a curve X over Fq. Let s(C) be the state complexity of C and set w(C): = min{k, n−k}, the Wolf upper bound on s(C). We introduce a numerical function R that depends on the gonality sequence of X and show
Results 11  20
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282,623