Contents -- Preface -- 1. Basics on error control -- 1.1 ABC on codes -- 1.1.1 Basic notations and terminology -- 1.1.2 Hamming weight and distance -- 1.1.3 Support of a set of vectors -- 1.1.4 Extending vectors -- 1.1.5 Ordering -- 1.1.6 Entropy -- 1.1.7 Systematic codes -- 1.1.8 Equivalent codes -- 1.1.9 New codes from old -- 1.1.10 Cyclic codes -- 1.2 Linear codes -- 1.2.1 Generator and check matrices for linear codes -- 1.2.2 The simplex codes and the Hamming codes -- 1.2.3 Equivalent and systematic linear codes -- 1.2.4 New linear codes from old -- 1.2.5 Cyclic linear and shortened cyclic linear codes -- 1.3 Distance distribution of codes -- 1.3.1 Definition of distance distribution -- 1.3.2 The MacWilliams transform -- 1.3.3 Binomial moment -- 1.3.4 Distance distribution of complementary codes -- 1.4 Weight distribution of linear codes -- 1.4.1 Weight distribution -- 1.4.2 Weight distribution of -extended codes -- 1.4.3 MacWilliams's theorem -- 1.4.4 A generalized weight distribution -- 1.4.5 Linear codes over larger fields -- 1.4.6 Weight distribution of cosets -- 1.4.7 Counting vectors in a sphere -- 1.4.8 Bounds on the number of code words of a given weight -- 1.5 The weight hierarchy -- 1.6 Principles of error detection -- 1.6.1 Pure detection -- 1.6.2 Combined correction and detection -- 1.7 Comments and references -- 2. Error detecting codes for the q-ary symmetric channel -- 2.1 Basic formulas and bounds -- 2.1.1 The q-ary symmetric channel -- 2.1.2 Probability of undetected error -- 2.1.3 The threshold -- 2.1.4 Alternative expressions for the probability of undetected error -- 2.1.5 Relations to coset weight distributions -- 2.2 Pue for a code and its MacWilliams transform -- 2.3 Conditions for a code to be satisfactory, good, or proper -- 2.3.1 How to determine if a polynomial has a zero.

2.3.2 Suffcient conditions for a code to be good -- 2.3.3 Necessary conditions for a code to be good or satisfactory -- 2.3.4 Suffcient conditions for a code to be proper -- 2.3.5 Large codes are proper -- 2.4 Results on the average probability -- 2.4.1 General results on the average -- 2.4.2 The variance -- 2.4.3 Average for special classes of codes -- 2.4.4 Average for systematic codes -- 2.5 The worst-case error probability -- 2.6 General bounds -- 2.6.1 Lower bounds -- 2.6.2 Upper bounds -- 2.6.3 Asymptotic bounds -- 2.7 Optimal codes -- 2.7.1 The dual of an optimal code -- 2.7.2 Copies of the simplex code -- 2.8 New codes from old -- 2.8.1 The -operation -- 2.8.2 Shortened codes -- 2.8.3 Product codes -- 2.8.4 Repeated codes -- 2.9 Probability of having received the correct code word -- 2.10 Combined correction and detection -- 2.10.1 Using a single code for correction and detection -- 2.10.2 Concatenated codes for error correction and detec- tion -- 2.10.3 Probability of having received the correct code word after decoding -- 2.11 Complexity of computing Pue(C -- p) -- 2.12 Particular codes -- 2.12.1 Perfect codes -- 2.12.2 MDS and related codes -- 2.12.3 Cyclic codes -- 2.12.4 Two weight irreducible cyclic codes -- 2.12.5 The product of two single parity check codes -- 2.13 How to nd the code you need -- 2.14 The local symmetric channel -- 2.15 Comments and references -- Chapter 3 Error detecting codes for the binary symmetric channel -- 3.1 A condition that implies "good" -- 3.2 Binary optimal codes for small dimensions -- 3.3 Modified codes -- 3.3.1 Adding/removing a parity bit -- 3.3.2 Even-weight subcodes -- 3.4 Binary cyclic redundancy check (CRC) codes -- 3.5 Particular codes -- 3.5.1 Reed-Muller codes -- 3.5.2 Binary BCH codes -- 3.5.3 Z4-linear codes -- 3.5.4 Self-complementary codes -- 3.5.5 Self-dual codes.

3.6 Binary constant weight codes -- 3.6.1 The codes m n -- 3.6.2 An upper bound -- 3.6.3 Lower bounds -- 3.7 Comments and references -- Chapter 4 Error detecting codes for asymmetric and other channels -- 4.1 Asymmetric channels -- 4.1.1 The Z-channel -- 4.1.2 Codes for the q-ary asymmetric channel -- 4.1.3 Diversity combining on the Z-channel -- 4.2 Coding for a symmetric channel with unknown charac- teristic -- 4.2.1 Bounds -- 4.2.2 Constructions -- 4.3 Codes for detection of substitution errors and transpo- sitions -- 4.3.1 ST codes -- 4.3.2 ISBN -- 4.3.3 IBM code -- 4.3.4 Digital codes with two check digits -- 4.3.5 Barcodes -- 4.4 Error detection for runlength-limited codes -- 4.5 Comments and references -- Bibliography -- Index.