MATH 256x. The Theory of Error-Correcting Codes (Fall 2013)

The general motivating setup from information theory for error-correcting block codes (as opposed to other kinds such as convolutional, let alone cryptographic: we’re aiming to protect against error, not eavesdropping). Natural languages such as English are very suboptimal error-correcting codes (fingerpuinting?); warning about real-world™ errors beyond the usual scope of the mathematical theory (eror-collecting colds). Coming attractions, drawing on combinatorics, symmetry and groups, linear algebra, finite geometry, invariant theory, orthogonal polynomials, etc. Example: the binary Golay code G23, suggested by the coincidence