17. Error-correcting codes
… flame of incandescent terrorOf which the tongues declareThe one discharge from sin and error
T. S. Eliot, ‘Little Gidding’ (1942)
TOPICS: Error-correction, minimum distance, linearity, bounds
TECHNIQUES: Linear algebra, projective geometry, number theory
ALGORITHMS: Encoding, syndrome decoding
This chapter begins with an example involving ‘guessing’ a number on the basis of information about it, some of which is ...