Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Table of Contents

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   Book Overview
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   Chapter 1 Cryptography and the Methodology of Provable Security
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   Chapter 2 Dynamical Systems Generated by Rational Functions
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   Chapter 3 Homotopy Methods for Equations over Finite Fields
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   Chapter 4 Three Constructions of Authentication/Secrecy Codes
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   Chapter 5 The Jacobi Model of an Elliptic Curve and Side-Channel Analysis
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   Chapter 6 Fast Point Multiplication on Elliptic Curves through Isogenies
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   Chapter 7 Interpolation of the Elliptic Curve Diffie-Hellman Mapping
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   Chapter 8 An Optimized Algebraic Method for Higher Order Differential Attack
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    Chapter 9 Fighting Two Pirates
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    Chapter 10 Copyright Control and Separating Systems
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    Chapter 11 Unconditionally Secure Homomorphic Pre-distributed Commitments
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    Chapter 12 A Class of Low-Density Parity-Check Codes Constructed Based on Reed-Solomon Codes with Two Information Symbols
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    Chapter 13 Relative Duality in MacWilliams Identity
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    Chapter 14 Good Expander Graphs and Expander Codes: Parameters and Decoding
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    Chapter 15 On the Covering Radius of Certain Cyclic Codes
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    Chapter 16 Unitary Error Bases: Constructions, Equivalence, and Applications
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    Chapter 17 Differentially 2-Uniform Cocycles — The Binary Case
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    Chapter 18 The Second and Third Generalized Hamming Weights of Algebraic Geometry Codes
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    Chapter 19 Error Correcting Codes over Algebraic Surfaces
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    Chapter 20 A Geometric View of Decoding AG Codes
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    Chapter 21 Performance Analysis of M-PSK Signal Constellations in Riemannian Varieties
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    Chapter 22 Improvements to Evaluation Codes and New Characterizations of Arf Semigroups
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    Chapter 23 Optimal 2-Dimensional 3-Dispersion Lattices
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    Chapter 24 On g -th MDS Codes and Matroids
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    Chapter 25 On the Minimum Distance of Some Families of ℤ 2 k -Linear Codes
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    Chapter 26 Quasicyclic Codes of Index ℓ over F q Viewed as F q [ x ]-Submodules of F q ℓ [ x ]/〈 x m −1〉
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    Chapter 27 Fast Decomposition of Polynomials with Known Galois Group