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→{{anchor|Minimum distance}}The distance d: Simplify link
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A larger distance allows for more error correction and detection.
For example, if we only consider errors that may change symbols of the sent codeword but never erase or add them, then the number of errors is the number of positions in which the sent codeword and the received word differ.
A code with distance <math>d</math> allows the receiver to detect up to <math>d-1</math> transmission errors since changing <math>d-1</math> positions of a codeword can never accidentally yield another codeword. Furthermore, if no more than <math>(d-1)/2</math> transmission errors occur, the receiver can uniquely decode the received word to a codeword. This is because every received word has at most one codeword at distance <math>(d-1)/2</math>. If more than <math>(d-1)/2</math> transmission errors occur, the receiver cannot uniquely decode the received word in general as there might be several possible codewords. One way for the receiver to cope with this situation is to use [[
=== Popular notation ===
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