Error-correcting code

Summary

An error-correcting code is a set of words of fixed length, the codewords, chosen far apart from each other in Hamming distance. A message is sent as a codeword; if a few symbols are corrupted on the way, the receiver still finds the nearest codeword. A code whose codewords are at distance at least $2t + 1$ from each other corrects any $t$ errors. Codes link combinatorics with algebra: good codes come from block designs, Hadamard matrices and finite fields. The node error-correcting code gives the precise definition.