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Thus, we can use the obtained encoding [[polynomial]] if we take our [[data]] to encode as the [[Row and column vectors|row vector]] <math>a = </math> <math>(a_{0,0}, a_{0,1}, a_{1,0}, a_{1,1}, a_{2,0}, a_{2,1}, a_{3,0}, a_{3,1})</math>. Encoding the [[Vector (mathematics and physics)|vector]] <math>m</math> to a length 15 message [[Vector (mathematics and physics)|vector]] <math>c</math> by multiplying <math>m</math> by the [[generator matrix]]
: <div style="text-align: center;"><math>
G = \begin{pmatrix}
1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\
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1 & 16 & 37 & 10 & 18 & 10 & 37 & 1 & 16 & 18 & 1 & 37 & 10 & 18 & 16
\end{pmatrix}
. </math></div>
For example, the encoding of information [[Vector (mathematics and physics)|vector]] <math>m = (1, 1, 1, 1, 1, 1, 1, 1)</math> gives the codeword <math>c = mG = (8, 8, 5, 9, 21, 3, 36, 31, 32, 12, 2, 20, 37, 33, 21)</math>.
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