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User:Rogério Brito/Books/Topics in Error Correcting Codes

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Topics in Error Correcting Codes

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Introduction
Forward error correction
Hamming bound
A Small Amount of Information Theory
Binary symmetric channel
Channel capacity
Noisy-channel coding theorem
Shannon's source coding theorem
Shannon–Hartley theorem
Mutual information
Preliminary Concepts
Block code
Repetition code
Linear code
Parity bit
Parity-check matrix
Generator matrix
Dual code
Hamming(7,4)
Decoding methods
List of Important Codes
Hamming code
Binary Golay code
Ternary Golay code
Cyclic code
BCH code
Polynomial code
Hadamard code
Quadratic residue code
Goppa code
Space–time code
Bar product (coding theory)
Reed–Muller code
Reed–Solomon error correction
Convolutional code
Turbo code
Low-density parity-check code
Important Bounds on Codes
Hamming bound
Singleton bound
Gilbert-Varshamov bound
Plotkin bound
Griesmer bound
Johnson bound
Applications and Related Concepts
Linear feedback shift register
RAID
Standard RAID levels
Berlekamp's algorithm
Berlekamp–Massey algorithm
Vandermonde matrix
Finite field
Finite field arithmetic