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Codes and Rings: Theory and Practice: Pure and Applied Mathematics, cartea -

Autor Minjia Shi, Adel Alahmadi, Patrick Solé
en Limba Engleză Paperback – 7 iun 2017
Codes and Rings: Theory and Practice is a systematic review of literature that focuses on codes over rings and rings acting on codes. Since the breakthrough works on quaternary codes in the 1990s, two decades of research have moved the field far beyond its original periphery. This book fills this gap by consolidating results scattered in the literature, addressing classical as well as applied aspects of rings and coding theory.
New research covered by the book encompasses skew cyclic codes, decomposition theory of quasi-cyclic codes and related codes and duality over Frobenius rings. Primarily suitable for ring theorists at PhD level engaged in application research and coding theorists interested in algebraic foundations, the work is also valuable to computational scientists and working cryptologists in the area.


  • Consolidates 20+ years of research in one volume, helping researchers save time in the evaluation of disparate literature
  • Discusses duality formulas in the context of Frobenius rings
  • Reviews decomposition of quasi-cyclic codes under ring action
  • Evaluates the ideal and modular structure of skew-cyclic codes
  • Supports applications in data compression, distributed storage, network coding, cryptography and across error-correction
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Specificații

ISBN-13: 9780128133880
ISBN-10: 0128133880
Pagini: 318
Dimensiuni: 152 x 229 x 20 mm
Editura: ELSEVIER SCIENCE
Seria Pure and Applied Mathematics


Public țintă

Ring theorists principally at PhD and research level interested in applications and coding theorist interested in algebraic foundations. Computer scientists and cryptologists interested in the protection of information.

Cuprins

1. Introduction2. Motivation3. Rings4. Distances5. Few Weights Codes6. Linear Codes7. Self-dual codes8. Cyclic codes9. Quasi-cyclic codes10. Quasi-Twisted Codes11. Generalized Quasi-Cyclic Codes12. Skew Cyclic Codes13. MDE Codes14. Convoluted Codes15. Character Sums

Recenzii

"This book is a treatise for coding theorists interested in algebraic foundations, working cryptologists and researchers looking for applications of pure mathematics. The authors explain properties of special rings like local rings, Galois rings, chain rings, Frobenius rings and skew polynomial rings, which frequently occur in applications. They also discuss several bounds (such as the sphere-packing bound, a Plotkin-like bound, a Singleton-like bound) for codes over rings with respect to various metrics." --Mathematical Reviews Clippings
"The authors point out how the subject is related to other fields e.g. combinatorics, number theory and ring theory. The book is very useful for references and can be also be used for the serious study of the subject. Ring theorists principally at PhD and research level, coding theorist interested in applications (computer scientists and cryptologists) could appreciate the collection and arrangement of research content of more than 250 references." --Zentralblatt MATH