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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combinatorics--