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During transmission, data may be altered, perhaps by random noise in the atmosphere. Coding messages allows the recipient to correct errors.

A message is a string of length $ n$ whose elements are either 0 or 1. In this project, all messages are assumed to have length $ n$. Thus a message will be an element of the vector space $ {\bf V}:={\{0,1\}}^{n}$.

The Hamming distance $ d$(v,w) of v and w is defined as the number of positions in which v and w differ.

The Hamming distance is a metric.

Bill Cherowitzo 2001-12-11