Example $3\mathrm{.}5$ The code $C=\{0000,1010,0101,1111\}$ is a linear block code of block length $n=4.$ This is a $(4,2)$ code. Observe that all the ten possible sums of the codewords

$0000+0000=0000,0000+1010=1010$

$0000+0101=0101$

$0000+1111=1111,1010+1010=0000$

$1010+0101=1111$

$1010+1111=0101,0101+0101=0000$

$0101+1111=1010$ and

$1111+1111=0000$