Hamming Distance

A Geometric Interpretation of Error correcting Codes

Hamming distance between two code words is defined as the number of different bit positions.

Let

and

then the Hamming distance between

The minimum distance decoder selects the code word "closest" in Hamming distance to the received message. A minimum distance decoder can correct m errors where m is the largest integer not to exceed

where

is the minimum distance between any two valid code words.

Example of Hamming Distances

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