Coding Theory and Applications

Name: Coding Theory and Applications | 5th International Castle Meeting, ICMCTA 2017, Vihula, Estonia, August 28-31, 2017, Proceedings
Brand: Springer
Price: 53.49 EUR
Availability: OnlineOnly

5th International Castle Meeting, ICMCTA 2017, Vihula, Estonia, August 28-31, 2017, Proceedings

Ángela I. Barbero Vitaly Skachek Øyvind Ytrehus(Herausgeber*in)

Springer (Verlag)

Erschienen am 22. August 2017

X, 297 Seiten

E-Book

PDF mit Wasserzeichen-DRM

Systemvoraussetzungen

978-3-319-66278-7 (ISBN)

53,49 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Wasserzeichen-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Inhalt

Intro
Preface
Organization
Contents
New Bounds for Linear Codes of Covering Radius 2
1 Introduction
2 An Upper Bound on the Length Function q(3,2)
3 Upper Bounds on the Length Function q(r,2), r5 Odd
4 Comparison with the Previously Known Results
References
Multidimensional Decoding Networks for Trapping Set Analysis
1 Introduction
2 Preliminaries
3 Multidimensional Network Framework
4 Trapping Set Characterization
5 Representations Yielding Transitivity
6 Conclusions
References
Erasure Correction and Locality of Hypergraph Codes
1 Introduction
2 Preliminaries
3 Bounds on Regular Hypergraph Codes
4 Bounds on Biregular Hypergraph Codes
5 Conclusions
References
Reed-Muller Codes: Information Sets from Defining Sets
1 Introduction
2 Preliminaries
3 Information Sets for Abelian Codes
4 Cyclic Codes as Two-Dimensional Cyclic Codes
5 Reed-Muller Codes
6 Information Sets for First-Order Reed-Muller Codes
7 Information Sets for Second-Order Reed-Muller Codes
8 Conclusions
References
Distance Properties of Short LDPC Codes and Their Impact on the BP, ML and Near-ML Decoding Performance
1 Introduction
2 Preliminaries
2.1 Ensembles of Binary and Binary Images of Nonbinary Regular LDPC Codes
2.2 QC LDPC Codes
3 Stopping Redundancy and Convergence to the ML Decoding Performance
4 Upper Bounds on ML and BP Decoding Error Probability for Ensembles of LDPC Codes
5 Simulation Results
6 Discussion
References
Decoding a Perturbed Sequence Generated by an LFSR
1 Introduction
2 A Decoding Problem
3 The Decoding Algorithm
References
A Construction of Orbit Codes
1 Introduction
2 Preliminaries
3 Our Construction
4 Open Questions
References
Analysis of Two Tracing Traitor Schemes via Coding Theory
1 Introduction
2 Open Tracing Traitor Schemes - How Do They Work?
3 How to Compare t-IPP Codes and t-IPP Family of Sets?
4 New Lower Bound on the Size of IPPS Codes
4.1 The Previous Results
4.2 Constant Weight Codes with Large Distance and Traceability Set System
References
Reliable Communication Across Parallel Asynchronous Channels with Glitches
1 Introduction
2 Problem Formulation
3 Related Work
4 Coding Schemes
4.1 Single-Code Based Coding Frameworks (W=1)
4.2 A Multiple-Code Based Coding Framework (W & 1)
4.3 A Comparison of the Efficiency of the Techniques
5 Summary
A Appendices
A.1 A Sketch of the Proof that the Transmission of Information Is Practically Error Free
A.2 The Proof that When Rmax Is Maximized, the Density of Ones Tends to 1+2
References
On the Kernel of Z2s-Linear Hadamard Codes
1 Introduction
2 Generalized Gray Map
3 Construction of Z2s-Linear Hadamard Codes
4 Partial Classification of Z2s-Linear Hadamard Codes
5 Conclusions
References
Random Network Coding over Composite Fields
1 Introduction
2 The Multicast Problem
3 Calculations in Composite Fields
4 Success Probability
5 Concluding Remarks
References
Bounding the Minimum Distance of Affine Variety Codes Using Symbolic Computations of Footprints
1 Introduction
2 Affine Variety Codes and the Footprint Bound
3 Code Words from the Klein Curve
3.1 Leading Monomial Equal to Y
3.2 Leading Monomial Equal to Y2
3.3 Leading Monomial Equal to XY
3.4 The Remaining Cases
4 Code Parameters
5 Concluding Remarks
References
On Binary Matroid Minors and Applications to Data Storage over Small Fields
1 Introduction
2 Preliminaries on LRCs and Matroids
2.1 Matroid Fundamentals
2.2 Fundamentals on Cyclic Flats
3 Sufficient Conditions for Uniformity
4 Criteria for Uniformity via Cyclic Flats
4.1 Minors Given by Restriction or Contraction only
4.2 Minors Given by both Restriction and Contraction
5 Stuctural Properties of Binary LRCs
6 Conclusions and Future Work
References
Absorbing Set Analysis of Codes from Affine Planes
1 Introduction
2 Preliminaries
3 Finite Euclidean LDPC Codes
3.1 Fully Absorbing Sets and Elementary Absorbing Sets
4 Conclusions
References
Asymptotic Bounds for the Sizes of Constant Dimension Codes and an Improved Lower Bound
1 Introduction
2 Preliminaries
3 Upper Bounds
3.1 Upper Bounds for Partial Spreads
4 The Linkage Construction Revisited
5 Asymptotic Bounds
6 Codes Better Than the MRD Bound
7 Conclusion
References
On Quasi-Abelian Complementary Dual Codes
1 Introduction
2 Preliminaries
2.1 Notations
2.2 Decompositions
3 Characterization and Enumeration of QACD Codes
4 Asymptotically Good Binary QAECD Codes of Index 3
References
Relative Generalized Hamming Weights and Extended Weight Polynomials of Almost Affine Codes
1 Introduction
2 Matroids, Demi-Matroids and Almost Affine Codes
2.1 Matroids and Demi-Matroids
2.2 Almost Affine Codes
2.3 Generalized Hamming Weights
3 Equivalent Formulations of Some Hamming Weights of Pairs of Codes
3.1 An Open Question Concerning Subcodes
4 Extended Weight Polynomials of Almost Affine Codes
References
On the Performance of Block Woven Codes Constructions with Row-Wise Permutations
1 Introduction
2 Block Woven Code Construction and Encoding
2.1 Simplified Deterministic Description
2.2 Proposed Code Ensemble
3 Decoding Algorithm
4 Distance Properties
5 Numerical results
6 Conclusion
References
New Lower Bounds on Error-Correcting Ternary, Quaternary and Quinary Codes
1 Introduction
2 Code Construction
3 Computer Search
4 New Lower Bounds
References
A State Space Approach to Periodic Convolutional Codes
1 Introduction
2 Preliminaries
2.1 Time-Invariant Convolutional Codes
2.2 Periodically Time-Varying Convolutional Codes
2.3 Distance Properties
3 State Space Realizations
4 Constructing Periodically Time-Varying Convolutional Codes
4.1 2-Periodic (3,2,2,1) Convolutional Code with Free Distance 4
5 Conclusions
References
Column Rank Distances of Rank Metric Convolutional Codes
1 Introduction
2 Convolutional Codes
3 Rank Metric Convolutional Codes
References
On Minimality of ISO Representation of Basic 2D Convolutional Codes
1 Introduction
2 Convolutional Codes
2.1 Polynomial Matrices
2.2 1D Convolutional Codes
2.3 2D Convolutional Codes
3 On Minimality of ISO Representations of Basic 2D Convolutional Codes
4 Conclusion
References
A New Construction of Minimum Distance Robust Codes
1 Introduction
2 Effectiveness Criterion for Robust Codes
3 Construction of Robust Codes with Distance
4 Summary
References
Constructions and Bounds for Batch Codes with Small Parameters
1 Introduction
2 Notations and Related Works
3 Batch Codes with r = 2 or t=2
3.1 Optimal Batch Codes with r 2 and t=2
3.2 Batch Codes and PIR Codes with t 2 and r=2
4 PIR Codes for Arbitrary t&2 and r&2
4.1 Case r|k
4.2 Case t=3 and rk
5 Bounds on the Dimension of a Batch Code
References
Author Index

Systemvoraussetzungen

Als PDF speichern Als Link merken