By introducing the mathematics for coding and the classical information theory,this book expoundsthe basic concepts and operations of network coding.Specifically,the applications of network coding inthe fields of network capacity,network security,and network storage are emphasized.A great number ofcoding methods and schemes are proposed.The operations of codes are elucidated with examples.Theadvantages and disadvantages of every code are analyzed in comparison to other codes.This monographis applicable for teachers,researchers and engineers in the field of information theory,information and communication technology,networking,etc.

Chapter 1 Coding Mathematics 1
1.1 Set Theory 1
1.1.1 The Rudiments of Set Theory 2
1.1.2 The Operation of Sets 4
1.1.3 Mapping 6
1.1.4 The Equivalence of Sets 7
1.1.5 The Classification of Sets 9
1.2 Abstract Algebra 11
1.2.1 Group 11
1.2.2 Ring 14
1.2.3 Field 19
1.2.4 Finite Field 21
1.2.5 Extension Fields 23
1.3 Vector Space 28
1.4 Probability Theory 30
1.4.1 Random Events and Probability 30
1.4.2 Random Variables 33
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