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Error-Correcting Codes : a Mathematical Introduction

Author: John Baylis
Publisher: Boca Raton, FL : Chapman & Hall/CRC, 2018.
Series: Chapman & Hall mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Baylis, John.
Error-Correcting Codes.
Boca Raton, FL : Chapman & Hall/CRC, 2018
(OCoLC)995766123
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: John Baylis
ISBN: 9781351449830 1351449834
OCLC Number: 1035845359
Description: 1 online resource
Contents: Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; 1: Setting the scene; 1.1 The problem; 1.2 The channel --
cause of the problem; 1.3 Cunning coding --
solution of the problem; 1.4 Exercises for Chapter 1; 2: Reducing the price; 2.1 Hamming's solution; 2.2 Can anything be done if two errors occur?; 2.3 An alternative use of Hamming codes --
erasures; 2.4 What really makes a code work? --
Hamming distance; 2.5 Further reading; 2.6 Exercises for Chapter 2; 3: Number theory --
arithmetic for codes; 3.1 Why number theory?; 3.2 Congruence and related ideas 3.3 Solving linear congruences3.4 A bit of arithmetic folklore; 3.5 The special rôle of primes; 3.6 A recreational interlude; 3.7 Zp and reciprocals; 3.8 Further reading; 3.9 Exercises for Chapter 3; 4: Block codes --
some constraints and some geometry; 4.1 The main problem; 4.2 Limitations on M; 4.3 Equivalent codes; 4.4 Distance isomorphic codes; 4.5 Geometry and Hamming space; 4.6 Perfect codes; 4.7 The Plotkin bound; 4.8 Exercises for Chapter 4; 5: The power of linearity; 5.1 The problem; 5.2 Linear codes --
their fundamental properties; 5.3 Linear algebra reminders 5.4 The generator matrix5.5 Cosets and the Slepian array; 5.6 The dual code and parity check matrix; 5.7 Syndrome decoding; 5.8 Equivalence of linear codes; 5.9 Erasure correction and syndromes; 5.10 Exercises for Chapter 5; 6: The Hamming family and friends; 6.1 Introduction; 6.2 Hamming codes; 6.3 Decoding Ham(r, q); 6.4 Simplex codes; 6.5 Optimal linear codes; 6.6 More on the structure of Hamming codes; 6.7 The cyclic property of Hamming codes; 6.8 Weight distributions; 6.9 Exercises for Chapter 6; 7: Polynomials for codes; 7.1 The first definitions; 7.2 Operations in F[X] 7.3 Factorization in Zp[X]7.4 Congruence of polynomials; 7.5 Rings and ideals; 7.6 Exercises for Chapter 7; 8: Cyclic codes; 8.1 Introduction; 8.2 The choice of modulus; 8.3 Generator matrices and generator polynomials; 8.4 Encoding by polynomials; 8.5 Syndromes and polynomials; 8.6 Parity checks and polynomials; 8.7 Cyclic codes and double-adjacent errors; 8.8 Cyclic golay codes; 8.9 Exercises for Chapter 8; 9: The Reed-Muller family of codes; 9.1 New codes from old; 9.2 Plotkin's construction; 9.3 The Reed-Muller family; 9.4 An alternative description of Reed-Muller codes 9.5 Hamming codes, first order Reed-Muller codes --
some connections9.6 Exercises for Chapter 9; Appendix: A Solutions, answers, hints; References; Index
Series Title: Chapman & Hall mathematics.
Responsibility: John Baylis.

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