| Description |
1 online resource : illustrations (black and white) |
| Series |
Discrete mathematics and its applications |
| Contents |
Cover; Half Title; Title Page; Copyright Page; Dedication; Contents; Preface; Acknowledgments; About the author; I: An elementary introduction to coding; 1 The concept of coding; 1.1 Bitstrings and binary operations; 1.2 The Hamming distance; 1.3 Binary codes; 1.4 Error-correcting codes in general; 1.5 The binary symmetric channel; 1.6 The sphere-packing bound; 2 Binary linear codes; 2.1 The concept of binary linear codes; 2.2 Block coding; 2.3 The effect of coding; 2.4 Duality; 2.5 Binary Hamming and Simplex codes; 2.6 Principle of duality; 3 General linear codes; 3.1 Prime fields |
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3.2 Finite fields3.3 Linear codes over finite fields; 3.4 Duality and orthogonal arrays; 3.5 Weight distribution; 3.6 The game of SET; 3.7 Syndrome decoding; 4 Singleton bound and Reed-Solomon codes; 5 Recursive constructions I; 5.1 Shortening and puncturing; 5.2 Concatenation; 6 Universal hashing; 7 Designs and the binary Golay code; 8 Shannon entropy; 9 Asymptotic results; 10 Three-dimensional codes, projective planes; 11 Summary and outlook; II: Theory and applications of codes; 12 Subfield codes and trace codes; 12.1 The trace; 12.2 Trace codes and subfield codes; 12.3 Galois closed codes |
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12.4 Automorphism groups13 Cyclic codes; 13.1 Some primitive cyclic codes of length 15; 13.2 Theory of cyclic codes; 13.3 Decoding BCH codes; 13.4 Constacyclic codes; 13.5 Remarks; 14 Recursive constructions, covering radius; 14.1 Construction X; 14.2 Covering radius; 15 The linear programming method; 15.1 Introduction to linear programming; 15.2 The Fourier transform; 15.3 Some explicit LP bounds; 15.4 The bound of four; 16 OA in statistics and computer science; 16.1 OA and independent random variables; 16.2 Linear shift register sequences; 16.3 Cryptography and S boxes |
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16.4 Two-point-based sampling16.5 Resilient functions; 16.6 Derandomization of algorithms; 16.7 Authentication and universal hashing; 17 The geometric description of linear codes; 17.1 Linear codes as sets of points; 17.2 Quadratic forms, bilinear forms and caps; 17.3 Caps: Constructions and bounds; 18 Additive codes and network codes; 18.1 Basic constructions and applications; 18.2 The cyclic theory of additive codes; 18.2.1 Code equivalence and cyclicity; 18.2.2 The linear case m = 1; 18.3 Additive quaternary codes: The geometric approach; 18.4 Quantum codes |
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18.5 Network codes and subspace codesIII: Codes and algebraic curves; 19 Introduction; 19.1 Polynomial equations and function fields; 19.2 Places of the rational function field; 20 Function fields, their places and valuations; 20.1 General facts; 20.2 Divisors and the genus; 20.3 The Riemann-Roch theorem; 20.4 Some hyperelliptic equations; 21 Determining the genus; 21.1 Algebraic extensions of function fields; 21.2 The hyperelliptic case; 21.3 The Kloosterman codes and curves; 21.4 Subrings and integrality; 21.5 The Riemann-Hurwitz formula; 22 AG codes, Weierstraß points and universal hashing |
| Notes |
CIP data; resource not viewed |
| Subject |
Coding theory.
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TECHNOLOGY & ENGINEERING -- Mobile & Wireless Communications.
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MATHEMATICS -- Combinatorics.
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Coding theory
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| Form |
Electronic book
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| ISBN |
9781482299830 |
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1482299836 |
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9781482299816 |
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148229981X |
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9781315321271 |
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1315321270 |
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9781482299823 |
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1482299828 |
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9781315371993 |
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1315371995 |
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