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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

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Cover of 'Applied Algebra, Algebraic Algorithms and Error-Correcting Codes'

Table of Contents

  1. Altmetric Badge
    Book Overview
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    Chapter 1 The Ubiquity of Reed-Muller Codes
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    Chapter 2 Self-dual Codes-Theme and Variations
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    Chapter 3 Design of Differential Space-Time Codes Using Group Theory
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    Chapter 4 Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms
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    Chapter 5 Self-dual Codes Using Image Restoration Techniques
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    Chapter 6 Low Complexity Tail-Biting Trellises of Self-dual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance
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    Chapter 7 Fq -Linear Cyclic Codes over Fq m: DFT Characterization
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    Chapter 8 Cyclic Projective Reed-Muller Codes
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    Chapter 9 Codes Identifying Sets of Vertices
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    Chapter 10 Duality and Greedy Weights of Linear Codes and Projective Multisets
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    Chapter 11 Type II Codes over IF2r
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    Chapter 12 On Senary Simplex Codes
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    Chapter 13 Optimal Double Circulant Z4-Codes
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    Chapter 14 Constructions of Codes from Number Fields
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    Chapter 15 On Generalized Hamming Weights for Codes over Finite Chain Rings
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    Chapter 16 Information Rates and Weights of Codes in Structural Matrix Rings
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    Chapter 17 On Hyperbolic Codes
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    Chapter 18 On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes
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    Chapter 19 Computing the Genus of a Class of Curves
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    Chapter 20 Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers
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    Chapter 21 Even Length Binary Sequence Families with Low Negaperiodic Autocorrelation
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    Chapter 22 On the Non-existence of (Almost-)Perfect Quaternary Sequences
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    Chapter 23 Maximal Periods of x2 + c in Fq
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    Chapter 24 On the Aperiodic Correlation Function of Galois Ring m-Sequences
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    Chapter 25 Euclidean Modules and Multisequence Synthesis
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    Chapter 26 On Homogeneous Bent Functions
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    Chapter 27 Partially Identifying Codes for Copyright Protection
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    Chapter 28 On the Generalised Hidden Number Problem and Bit Security of XTR
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    Chapter 29 Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
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    Chapter 30 An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products
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    Chapter 31 Algorithms for Large Integer Matrix Problems
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    Chapter 32 On the Identification of Vertices and Edges Using Cycles
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    Chapter 33 On Algebraic Soft Decision Decoding of Cyclic Binary Codes
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    Chapter 34 Lifting Decoding Schemes over a Galois Ring
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    Chapter 35 Sufficient Conditions on Most Likely Local Sub-codewords in Recursive Maximum Likelihood Decoding Algorithms
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    Chapter 36 A Unifying System-Theoretic Framework for Errors-and-Erasures Reed-Solomon Decoding
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    Chapter 37 An Algorithm for Computing Rejection Probability of MLD with Threshold Test over BSC
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    Chapter 38 Cartan’s Characters and Stairs of Characteristic Sets
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    Chapter 39 On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2
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    Chapter 40 Algebraic Constructions for PSK Space-Time Coded Modulation
Attention for Chapter 19: Computing the Genus of a Class of Curves
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Chapter title
Computing the Genus of a Class of Curves
Chapter number 19
Book title
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Published by
Springer Berlin Heidelberg, January 2001
DOI 10.1007/3-540-45624-4_19
Book ISBNs
978-3-54-042911-1, 978-3-54-045624-7
Authors

M. C. Rodríguez-Palánquex, L. J. García-Villalba, I. Luengo-Velasco

Editors

Serdar Boztaş, Igor E. Shparlinski