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Combinatorics by Peter J. Cameron

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17. Error-correcting codes

… flame of incandescent terrorOf which the tongues declareThe one discharge from sin and error

T. S. Eliot, ‘Little Gidding’ (1942)

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TOPICS: Error-correction, minimum distance, linearity, bounds

TECHNIQUES: Linear algebra, projective geometry, number theory

ALGORITHMS: Encoding, syndrome decoding

CROSS-REFERENCES: Packing and covering (Chapter 8); projective geometry (Chapter 9); designs (Chapter 16)

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This chapter begins with an example involving ‘guessing’ a number on the basis of information about it, some of which is ...

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