An Hamming (n,k) code is the set of all n-simbols binary word that satisfy the relation...

(1)

... where...

a) is a n bit row vector

b) is a n-k bit column vector called symdrome

c) is the n-k bit 'null vector'

d) is the n x k bit 'parity check' matrix

An example of parity 7 x 4 Hamming parity check matrix is the following...

A 7 x 4 Hamming code can correct any single error that occurred in a 7 bits transmitted word...

Kind regards