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Foundations of Coding Theory

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Product Details

  • ISBN-13: 9789401023009
  • Publisher: Springer Netherlands
  • Publication date: 12/31/2013
  • Series: Episteme Series , #1
  • Edition description: Softcover reprint of the original 1st ed. 1974
  • Pages: 236

Table of Contents

I / Introduction.- 1. Basic Problems of Abstract Coding Theory.- 1. The Setting for the Study.- 2. Models.- 3. The Setting for the Definitions.- 4. Definitions.- 5. A Guide to the Book.- 2. Basic Properties of Error-Correcting Codes.- 1. Introduction.- 2. Description of the Error Patterns.- 3. Correcting Ability and Decodability.- 4. Synchronizability and Comma-Freedom.- II / Theoretical Studies.- Overview.- 3. A Study of Error-Correcting Codes, I.- 1. Introduction.- 2. Preliminaries.- 3. Mappings Associated with a Code.- 4. Irredundant and Precorrecting Codes.- 5. Correcting Codes.- 4. A Study of Error-Correcting Codes, II: Decodability Properties.- 1. Introduction.- 2. Codes and Mappings.- 3. Correcting Codes.- 4. Decodable Codes.- 5. Prompt Codes.- 5. A Study of Error-Correcting Codes, III: Synchronizability and Comma-Freedom.- 1. Introduction.- 2. Synchronizable Codes.- 3. Comma-Free Codes.- 4. Diagrams and Tables.- 6. A Study of Error-Correcting Codes, IV: Code Properties and Unambiguous Sets.- 1. Introduction.- 2. Extension of Concepts.- 3. Scansions.- 4. Code-Related Properties.- 7. Some General Results of Abstract Coding Theory with Applications to the Study of Codes for the Correction of Synchronization Errors.- 1. Introduction.- 2. Separation for a Binary Relation.- 3. Error-Correcting Capability.- 4. Error-Decoding Capability.- 5. Error-Limiting Capability.- 6. On the Levenshtein Distance.- 7. Error-Correcting for the Levenshtein Metric.- 8. A Sufficient Condition for Decodability.- III / Tests and Constructions.- Overview.- 8. The Sardinas/Patterson and Levenshtein Theorems.- 1. Introduction.- 2. The Residual Quotient.- 3. Characterization of—n(C, D).- 4. Unique Decipherability.- 5. A Finiteness Condition. Codes with Bounded Delay.- 6. Synchronizable Codes.- 7. Some Numerical Bounds.- 9. Generalization of Tests for Certain Properties of Variable-Length Codes.- 1. Introduction.- 2. Definitions and Examples.- 3. A Construction Involving Gauged Sets.- 4. Tests for Certain Properties of Codes.- 5. Application of the Tests to Example Codes.- 10. On a Family of Error Correcting and Synchronizable Codes.- 1. Introduction.- 2. Definitions.- 3. Code Properties.- 4. Properties of N-Sets.- 5. Examples.- 11. A Family of Codes for the Correction of Substitution and Synchronization Errors.- 1. Introduction.- 2. The Codes Anc.- 3. Some General Results.- 4. The Codes Anc have Properties (1) and (2).- Epilogue.- Selected Bibliography on Coding Theory (1957–1968) from Parke Mathematical Laboratories.- References.- Index of Authors.- Index of Subjects.

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