Codes: An Introduction to Information Communication and Cryptography

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Springer Science & Business Media, Dec 16, 2008 - Computers - 274 pages
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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.
 

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LibraryThing Review

User Review  - Ndkchk - LibraryThing

The "Introduction" in the title should be somewhat stressed. It's good, but doesn't go that much into depth about anything. Personally, I would have preferred somewhat more code and somewhat less math ... Read full review

Contents

Prefixfree codes
12
Economical coding
27
Data compression
47
Noisy channels
73
The problem of reliable communication
89
The noisy coding theorems
107
Linear codes
123
Algebraic coding theory
141
The development of cryptography
179
Cryptography in theory and practice
191
The RSA cryptosystem
207
Cryptography and calculation
221
Elliptic curve cryptography
237
Answers to oddnumbered exercises
254
Index
270
Copyright

Coding natural languages
163

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