An error-correcting code (see Section 4.2) is a method for redundantly encoding information so that the information can still be retrieved even in the face of some errors in transmission/storage. The...

An error-correcting code (see Section 4.2) is a method for redundantly encoding information so that the information can still be retrieved even in the face of some errors in transmission/storage. The Hamming code is a particular errorcorrecting code for 4-bit chunks of information. The Hamming code can be described using matrix multiplication: given a message m ∈ {0, 1} 4 , we encode m as mG mod 2, where