Skip to main content
  • Textbook
  • © 2008

Codes: An Introduction to Information Communication and Cryptography

Authors:

  • By the author of the highly-praised text Discrete Mathematics
  • Introduces the mathematical theories that find many applications in modern technology, bringing readers up-to-date with topics of great current interest, both in practice and in theory
  • Clear and concise, with complete proofs of the results and a wealth of examples and exercises to test understanding
  • Assumes only a modest mathematical background and provides careful explanations of the basic principles without recourse to jargon
  • Includes supplementary material: sn.pub/extras
  • Request lecturer material: sn.pub/lecturer-material

Part of the book series: Springer Undergraduate Mathematics Series (SUMS)

Buy it now

Buying options

eBook USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 37.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (15 chapters)

  1. Front Matter

    Pages 1-9
  2. Coding and its uses

    • Norman L. Biggs
    Pages 1-11
  3. Prefix free codes

    • Norman L. Biggs
    Pages 1-14
  4. Economical coding

    • Norman L. Biggs
    Pages 1-20
  5. Data compression

    Pages 1-26
  6. Noisy channels

    • Norman L. Biggs
    Pages 1-16
  7. The problem of reliable communication

    • Norman L. Biggs
    Pages 1-17
  8. The noisy coding theorems

    • Norman L. Biggs
    Pages 1-16
  9. Linear codes

    • Norman L. Biggs
    Pages 1-18
  10. Algebraic coding theory

    • Norman L. Biggs
    Pages 1-22
  11. Coding natural languages

    • Norman L. Biggs
    Pages 1-16
  12. The development of cryptography

    • Norman L. Biggs
    Pages 1-12
  13. Cryptography in theory and practice

    • Norman L. Biggs
    Pages 1-16
  14. The RSA cryptosystem

    • Norman L. Biggs
    Pages 1-14
  15. Cryptography and calculation

    • Norman L. Biggs
    Pages 1-16
  16. Elliptic curve cryptography

    • Norman L. Biggs
    Pages 1-17
  17. Back Matter

    Pages 1-18

About this book

Many people do not realise that mathematics provides the foundation for the devices we use to handle information in the modern world. Most of those who do know probably think that the parts of mathematics involvedare quite ‘cl- sical’, such as Fourier analysis and di?erential equations. In fact, a great deal of the mathematical background is part of what used to be called ‘pure’ ma- ematics, indicating that it was created in order to deal with problems that originated within mathematics itself. It has taken many years for mathema- cians to come to terms with this situation, and some of them are still not entirely happy about it. Thisbookisanintegratedintroductionto Coding.Bythis Imeanreplacing symbolic information, such as a sequence of bits or a message written in a naturallanguage,byanother messageusing (possibly) di?erentsymbols.There are three main reasons for doing this: Economy (data compression), Reliability (correction of errors), and Security (cryptography). I have tried to cover each of these three areas in su?cient depth so that the reader can grasp the basic problems and go on to more advanced study. The mathematical theory is introduced in a way that enables the basic problems to bestatedcarefully,butwithoutunnecessaryabstraction.Theprerequisites(sets andfunctions,matrices,?niteprobability)shouldbefamiliartoanyonewhohas taken a standard course in mathematical methods or discrete mathematics. A course in elementary abstract algebra and/or number theory would be helpful, but the book contains the essential facts, and readers without this background should be able to understand what is going on. vi Thereareafewplaceswherereferenceismadetocomputeralgebrasystems.

Reviews

From the reviews:

"This undergraduate textbook is a pleasure to read. … The author has a sense of humor, and he is not afraid to use it. The examples are very well chosen. … This very enjoyable book deserves many readers." (Miklós Bóna, The Mathematical Association of America, September, 2008)

"This is a clearly and carefully written introduction into information theory, coding theory and cryptography. … Due to the many motivating explanation, the numerous number of examples (for nearly every definition, concept and result) … and the many suggestions for further reading this book is, in my opinion, very suitable as well as for beginners in the field … . I can very much recommend this book to interested bachelor students as well as to lecturers on this subject." (Ralph-Hardo Schulz, Zentralblatt MATH, Vol. 1148, 2008)

"Coding here refers to the formal transcription of abstract information with the aim of achieving some combination of efficiency, reliability, and perhaps security. … Codes provides the student an initiation and shows the author’s great talent for mathematical exposition clearly propelled by big ideas. … will be valuable for academic libraries. Summing Up: Highly recommended. Advanced academic audiences, upper-division undergraduates through researchers/faculty." (D. V. Feldman, Choice, Vol. 46 (8), April, 2009)

"There are indeed substantial texts devoted to compression, coding systems of various sorts, and encryption. This text brings these three components together in a unified context and provides a basic, mathematically inclined introduction to each. … There is a reasonable amount of worked examples and exercises in the text. … This book could serve as a nice introduction to coding theory for computer science or electrical engineering students … and for mathematics students interested in computing and applied mathematics." (Jeffrey Putnam, ACM Computing Reviews, September, 2009)

Authors and Affiliations

  • and Political Science, Dept. Statistics & Mathematics, London School of Economics, London, United Kingdom

    N.L. Biggs

Bibliographic Information

Buy it now

Buying options

eBook USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 37.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access