The Mathematical Theory of Coding
eBook - PDF

The Mathematical Theory of Coding

  1. 368 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

The Mathematical Theory of Coding

Book details
Table of contents
Citations

About This Book

The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.

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Yes, you can access The Mathematical Theory of Coding by Ian F. Blake,Ronald C. Mullin in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
ISBN
9781483260594
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics

Table of contents

  1. Front Cover
  2. The Mathematical Theory of Coding
  3. Copyright Page
  4. Table of Contents
  5. Dedication
  6. Preface
  7. Acknowledgments
  8. Chapter 1. Finite Fields and Coding Theory
  9. Chapter 2. Combinatorial Constructions and Coding
  10. Chapter 3. Coding and Combinatorics
  11. Chapter 4. The Structure of Semisimpie Rings
  12. Chapter 5. Group Representations
  13. Chapter 6. Group Codes for the Gaussian Channel
  14. APPENDIX A: The Möbius Inversion Formula
  15. APPENDIX B: Lucas's Theorem
  16. APPENDIX C: The Mathieu Groups
  17. References
  18. Index