In
combinatorics, there exists a
subset of the
vectors
from a
vector space over a
finite field. These
vectors are collectively called "
code words" and the
finite field is usually
GF(2), although there are useful
codes over GF(3) and GF(4) as well.
In an
error-correcting code, the
code words are
chosen such that the "
distance" between them is
maximized, thus small transmission
errors can be recovered by
interpreting
the received
vector as the
nearest code word.
See
Hamming distance.
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