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Cryptography, Information Theory, and Error-Correction. Aiden A. Bruen
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Информация о произведении:
Название
Cryptography, Information Theory, and Error-Correction
Автор произведения
Aiden A. Bruen
Жанр
Зарубежная компьютерная литература
Серия
Издательство
Зарубежная компьютерная литература
Год выпуска
0
isbn
9781119582403
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for Correction and Detection
18.4 Hadamard Matrices
18.5 Mariner, Hadamard, and Reed–Muller
18.6 Reed–Muller Codes
18.7 Block Designs
18.8 The Rank of Incidence Matrices
18.9 The Main Coding Theory Problem, Bounds
18.10 Update on the Reed–Muller Codes: The Proof of an Old Conjecture
18.11 Problems
18.12 Solutions
Chapter 19: Finite Fields, Modular Arithmetic, Linear Algebra, and Number Theory
19.1 Modular Arithmetic
19.2 A Little Linear Algebra
19.3 Applications to RSA
19.4 Primitive Roots for Primes and Diffie–Hellman
19.5 The Extended Euclidean Algorithm
19.6 Proof that the RSA Algorithm Works
19.7 Constructing Finite Fields
19.8 Pollard's
p
-1 Factoring Algorithm
19.9 Latin Squares
19.10 Computational Complexity, Turing Machines, Quantum Computing
19.11 Problems
19.12 Solutions
Note
Chapter 20: Introduction to Linear Codes
20.1 Repetition Codes and Parity Checks
20.2 Details of Linear Codes
20.3 Parity Checks, the Syndrome, and Weights
20.4 Hamming Codes, an Inequality
20.5 Perfect Codes, Errors, and the BSC
20.6 Generalizations of Binary Hamming Codes
20.7 The Football Pools Problem, Extended Hamming Codes
20.8 Golay Codes
20.9 McEliece Cryptosystem
20.10 Historical Remarks
20.11 Problems
20.12 Solutions
Chapter 21: Cyclic Linear Codes, Shift Registers, and CRC
21.1 Cyclic Linear Codes
21.2 Generators for Cyclic Codes
21.3 The Dual Code
21.4 Linear Feedback Shift Registers and Codes
21.5 Finding the Period of a LFSR
21.6 Cyclic Redundancy Check (CRC)
21.7 Problems
21.8 Solutions
Chapter 22: Reed‐Solomon and MDS Codes, and the Main Linear Coding Theory Problem (LCTP)
22.1 Cyclic Linear Codes and Vandermonde
22.2 The Singleton Bound for Linear Codes
22.3 Reed–Solomon Codes
22.4 Reed‐Solomon Codes and the Fourier Transform Approach
22.5 Correcting Burst Errors, Interleaving
22.6 Decoding Reed‐Solomon Codes, Ramanujan, and Berlekamp–Massey
22.7 An Algorithm for Decoding and an Example
22.8 Long MDS Codes and a Partial Solution of a 60 Year‐Old Problem
22.9 Problems
22.10 Solutions
Chapter 23: MDS Codes, Secret Sharing, and Invariant Theory
23.1 Some Facts Concerning MDS Codes
23.2 The Case
k = 2
, Bruck Nets
23.3 Upper Bounds on MDS Codes, Bruck–Ryser
23.4 MDS Codes and Secret Sharing Schemes
23.5 MacWilliams Identities, Invariant Theory
23.6 Codes, Planes, and Blocking Sets
23.7 Long Binary Linear Codes of Minimum Weight at Least 4
23.8 An Inverse Problem and a Basic Question in Linear Algebra
Chapter 24: Key Reconciliation, Linear Codes, and New Algorithms
24.1 Symmetric and Public Key Cryptography
24.2 General Background
24.3 The Secret Key and the Reconciliation Algorithm
24.4 Equality of Remnant Keys: The Halting Criterion
24.5 Linear Codes: The Checking Hash Function
24.6 Convergence and Length of Keys
24.7
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