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Algebraic curves and applications to coding theory.
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- Subject Terms:
- Document Type:
text
- Language:
English
Chinese
- Additional Information
- Contributors:
Yan, Cho Hung.; Chinese University of Hong Kong Graduate School. Division of Mathematics.
- Publication Date:
1998
- Collection:
The Chinese University of Hong Kong: CUHK Digital Repository / 香港中文大學數碼典藏
- Abstract:
by Yan Cho Hung. ; Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. ; Includes bibliographical references (leaves 122-124). ; Abstract also in Chinese. ; Chapter 1 --- Complex algebraic curves --- p.6 ; Chapter 1.1 --- Foundations --- p.6 ; Chapter 1.1.1 --- Hilbert Nullstellensatz --- p.6 ; Chapter 1.1.2 --- Complex algebraic curves in C2 --- p.9 ; Chapter 1.1.3 --- Complex projective curves in P2 --- p.11 ; Chapter 1.1.4 --- Affine and projective curves --- p.13 ; Chapter 1.2 --- Algebraic properties of complex projective curves in P2 --- p.16 ; Chapter 1.2.1 --- Intersection multiplicity --- p.16 ; Chapter 1.2.2 --- Bezout's theorem and its applications --- p.18 ; Chapter 1.2.3 --- Cubic curves --- p.21 ; Chapter 1.3 --- Topological properties of complex projective curves in P2 --- p.23 ; Chapter 1.4 --- Riemann surfaces --- p.26 ; Chapter 1.4.1 --- Weierstrass &-function --- p.26 ; Chapter 1.4.2 --- Riemann surfaces and examples --- p.27 ; Chapter 1.5 --- Differentials on Riemann surfaces --- p.28 ; Chapter 1.5.1 --- Holomorphic differentials --- p.28 ; Chapter 1.5.2 --- Abel's Theorem for tori --- p.31 ; Chapter 1.5.3 --- The Riemann-Roch theorem --- p.32 ; Chapter 1.6 --- Singular curves --- p.36 ; Chapter 1.6.1 --- Resolution of singularities --- p.37 ; Chapter 1.6.2 --- The topology of singular curves --- p.45 ; Chapter 2 --- Coding theory --- p.48 ; Chapter 2.1 --- An introduction to codes --- p.48 ; Chapter 2.1.1 --- Efficient noiseless coding --- p.51 ; Chapter 2.1.2 --- The main coding theory problem --- p.56 ; Chapter 2.2 --- Linear codes --- p.58 ; Chapter 2.2.1 --- Syndrome decoding --- p.63 ; Chapter 2.2.2 --- Equivalence of codes --- p.65 ; Chapter 2.2.3 --- An introduction to cyclic codes --- p.67 ; Chapter 2.3 --- Special linear codes --- p.71 ; Chapter 2.3.1 --- Hamming codes --- p.71 ; Chapter 2.3.2 --- Simplex codes --- p.72 ; Chapter 2.3.3 --- Reed-Muller codes --- p.73 ; Chapter 2.3.4 --- BCH codes --- p.75 ; Chapter 2.4 --- Bounds on codes --- p.77 ; Chapter 2.4.1 --- Spheres ...
- File Description:
print; 124 leaves; 30 cm.
- Relation:
cuhk:322199; http://library.cuhk.edu.hk/record=b5889656; https://repository.lib.cuhk.edu.hk/en/item/cuhk-322199
- Online Access:
http://library.cuhk.edu.hk/record=b5889656
https://repository.lib.cuhk.edu.hk/en/item/cuhk-322199
- Rights:
Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)
- Accession Number:
edsbas.259BC72E
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