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On Goppa codes and Weierstrass gaps at several points
 DES CODES CRYPTOGR
, 2005
"... We generalize results of Homma and Kim [2001, J. Pure Appl. Algebra 162, 273–290] concerning an improvement on the Goppa bound on the minimum distance of certain Goppa codes. ..."
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Cited by 25 (5 self)
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We generalize results of Homma and Kim [2001, J. Pure Appl. Algebra 162, 273–290] concerning an improvement on the Goppa bound on the minimum distance of certain Goppa codes.
Consecutive Weierstrass gaps and minimum distance of Goppa codes
 J. Pure Appl. Algebra
, 1993
"... Abstract: We prove that if there are consecutive gaps at a rational point on a smooth curve defined over a finite field, then one can improve the usual lower bound on the minimum distance of certain algebraicgeometric codes defined using a multiple of the point. A qary linear code of length n and ..."
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Cited by 23 (0 self)
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Abstract: We prove that if there are consecutive gaps at a rational point on a smooth curve defined over a finite field, then one can improve the usual lower bound on the minimum distance of certain algebraicgeometric codes defined using a multiple of the point. A qary linear code of length n
Weierstrass pairs and minimum distance of Goppa codes, Des
 Codes and Cryptog
, 1999
"... Abstract. We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code which has minimum distance greater than the usual lower bound. We determine the Weierstrass gap set of a pair of any two Weierstrass points on a Hermitian curve and use this t ..."
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Cited by 24 (9 self)
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Abstract. We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code which has minimum distance greater than the usual lower bound. We determine the Weierstrass gap set of a pair of any two Weierstrass points on a Hermitian curve and use
On Weierstrass semigroups and the redundancy of improved geometric Goppa codes
 IEEE Trans. Inform. Theory
, 1999
"... Abstract. Improved geometric Goppa codes have a smaller redundancy and the same bound on the minimum distance as ordinary algebraic geometry codes. For an asymptotically good sequence of function fields we give a formula for the redundancy. 1. ..."
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Cited by 6 (1 self)
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Abstract. Improved geometric Goppa codes have a smaller redundancy and the same bound on the minimum distance as ordinary algebraic geometry codes. For an asymptotically good sequence of function fields we give a formula for the redundancy. 1.
On Weierstrass semigroups at one or several points
"... Let X be a nonsingular, projective, irreducible curve of genus g> 0, defined over a field K which we assume to be algebraically closed in K(X) (hence K is the full field of constants of the function field K(X), one also says that the ..."
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Let X be a nonsingular, projective, irreducible curve of genus g> 0, defined over a field K which we assume to be algebraically closed in K(X) (hence K is the full field of constants of the function field K(X), one also says that the
On Weierstrass points and optimal curves
, 1997
"... We use Weierstrass Point Theory and Frobenius orders to prove the uniqueness (up to isomorphism) of some optimal curves. ..."
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Cited by 18 (11 self)
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We use Weierstrass Point Theory and Frobenius orders to prove the uniqueness (up to isomorphism) of some optimal curves.
Decoding geometric Goppa codes using an extra place
 IEEE TRANS. INFORM. THEORY
, 1992
"... Decoding geometric Goppa codes can be reduced to solving the key congruence of a received word in an affine ring. If the code length is smaller than the number of rational points on the curve, then this method can correct up to 1/2 (d∗ − 1) − s errors, where d∗ is the designed minimum distance of t ..."
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Cited by 14 (5 self)
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Decoding geometric Goppa codes can be reduced to solving the key congruence of a received word in an affine ring. If the code length is smaller than the number of rational points on the curve, then this method can correct up to 1/2 (d∗ − 1) − s errors, where d∗ is the designed minimum distance
Weierstrass Points And Simple Geodesics
, 1996
"... . We investigate the set of tangent vectors at a Weierstrass point tangent to complete simple geodesics, which we think of as an infinitesimal version of the Birman Series set, showing that they are a Cantor set of Hausdorff dimension 1. The gaps in the Cantor set are classified in terms of the topo ..."
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Cited by 6 (0 self)
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. We investigate the set of tangent vectors at a Weierstrass point tangent to complete simple geodesics, which we think of as an infinitesimal version of the Birman Series set, showing that they are a Cantor set of Hausdorff dimension 1. The gaps in the Cantor set are classified in terms
A generalized floor bound for the minimum distance of geometric Goppa codes
 J. Pure Appl. Algebra
"... Abstract. We prove a new bound for the minimum distance of geometric Goppa codes that generalizes two previous improved bounds. We include examples of the bound to one and two point codes over both the Suzuki and Hermitian curves. 1. ..."
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Cited by 4 (0 self)
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Abstract. We prove a new bound for the minimum distance of geometric Goppa codes that generalizes two previous improved bounds. We include examples of the bound to one and two point codes over both the Suzuki and Hermitian curves. 1.
Results 1  10
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