On the floor and the ceiling of a divisor
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The floor and the ceiling of a divisor supported by collinear places of the Hermitian function field are determined and are found to give new bounds for the minimum distance of algebraic geometry codes.About:
This article is published in Finite Fields and Their Applications.The article was published on 2006-01-01 and is currently open access. It has received 16 citations till now. The article focuses on the topics: Divisor summatory function & Zero divisor.read more
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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 15th International Symposium, AAECC-15, Toulouse, France, May 12-16, 2003, Proceedings
TL;DR: This work discusses the construction of Authentication/Secrecy Codes, performance analysis of M-PSK Signal Constellations in Riemannian Varieties, and fast Decomposition of Polynomials with Known Galois Group.
Journal ArticleDOI
Coset bounds for algebraic geometric codes
Iwan Duursma,Seungkook Park +1 more
TL;DR: New coset bounds for algebraic geometric codes are developed that improve both floor bounds and order bounds and provide for the first time a connection between the two types of bounds.
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On the parameters of Algebraic Geometry codes related to Arf semigroups
TL;DR: The Feng-Rao bound on the minimum distance of one-point algebraic-geometry codes C/sub /spl Omega//(P, /spl rho//sub t/Q) is computed and the dimension of the improved geometric Goppa codes related to these are provided.
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Coset bounds for algebraic geometric codes
Iwan Duursma,Seungkook Park +1 more
TL;DR: Lower bounds on the degree of a divisor A such that A and A-C belong to specified semigroups of divisors were obtained in this paper for two-point codes on general Hermitian and Suzuki curves.
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Distance bounds for algebraic geometric codes
TL;DR: In this paper, the van Lint and Wilson AB method was used to obtain improvements of the Goppa lower bound for the minimum distance of an algebraic geometric code, and the main methods divide into two categories, and all but a few of the known bounds are special cases of either the Lundell-McCullough floor bound or the Beelen order bound.
References
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Geometry of algebraic curves
TL;DR: This chapter discusses Brill-Noether theory on a moving curve, and some applications of that theory in elementary deformation theory and in tautological classes.
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Algebraic Function Fields and Codes
TL;DR: This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded and contains numerous exercises that help the reader to understand the basic material.
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Generalized Hamming weights for linear codes
TL;DR: By viewing the minimum Hamming weight as a certain minimum property of one-dimensional subcodes, a generalized notion of higher-dimensional Hamming weights is obtained, which characterize the code performance on the wire-tap channel of type II.
Book
Handbook Of Coding Theory
TL;DR: This work focuses on the algebraic theory of concolutional codes, a type of binary codes based on residue codes, and its application to discrete geometry.
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Algebraic Curves and Riemann Surfaces
TL;DR: Riemann surfaces: Basic definitions Functions and maps More examples of Riemann surface integration on RiemANN surfaces Integration on RANNs: Divisors and meromorphic functions Algebraic curves and the riemann-Roch theorem Applications of the Abel's theorem Sheaves and Cech cohomology Invertible sheaves, line bundles and line bundles.