
Theory of Codes
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Content
- Front Cover
- Theory of Codes
- Copyright Page
- Contents
- Preface
- Chapter 0. Preliminaries
- 0 Introduction
- 1 Notation
- 2 Monoids
- 3 Words
- 4 Automata
- 5 Ideals in a Monoid
- 6 Semirings and Matrices
- 7 Formal Series
- 8 Permutation Groups
- 9 Notes
- Chapter 1. Codes
- 0 Introduction
- 1 Definitions
- 2 Codes and Submonoids
- 3 A Test for Codes
- 4 Measure of a Code
- 5 Complete Sets
- 6 Composition
- 7 Exercises
- 8 Notes
- Chapter 2. Prefix Codes
- 0 Introduction
- 1 Prefix Codes
- 2 The Automaton of a Prefix Code
- 3 Maximal Prefix Codes
- 4 Operations on Prefix Codes
- 5 Semaphore Codes
- 6 Synchronous Codes
- 7 Average Length
- 8 Deciphering Delay
- 9 Exercises
- 10 Notes
- Chapter 3. Biprefix Codes
- 0 Introduction
- 1 Parses
- 2 Maximal Biprefix Codes
- 3 Degree
- 4 Kernel
- 5 Finite Maximal Biprefix Codes
- 6 Exercises
- 7 Notes
- Chapter 4. Automata
- 0 Introduction
- 1 Automata
- 2 Flower Automaton
- 3 Monoids of Unambiguous Relations
- 4 Rank and Minimal Ideal
- 5 Very Thin Codes
- 6 Group and Degree of a Code
- 7 Synchronization of Semaphores
- 8 Exercises
- 9 Notes
- Chapter 5. Groups of Biprefix Codes
- 0 Introduction
- 1 Group Codes
- 2 Automata of Biprefix Codes
- 3 Depth
- 4 Groups of Finite Biprefix Codes
- 5 Examples
- 6 Exercises
- 7 Notes
- Chapter 6. Densities
- 0 Introduction
- 1 Densities
- 2 Probabilities over a Monoid
- 3 Contexts
- 4 Exercises
- 5 Notes
- Chapter 7. Conjugacy
- 0 Introduction
- 1 Circular Codes
- 2 Limited Codes
- 3 Length Distributions
- 4 Factorizations of Free Monoids
- 5 Finite Factorizations
- 6 Exercises
- 7 Notes
- Chapter 8. Polynomial of a Code
- 0 Introduction
- 1 Factorizing Codes
- 2 Determinants
- 3 State Space
- 4 Evaluation of the Polynomials
- 5 Proof of the Theorem
- 6 Commutative Equivalence
- 7 Complete Reducibility
- 8 Exercises
- 9 Notes
- References
- Index
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