$y_1=(00010110)$,and the parity check matrix $\mathbf H$ is
$\mathbf H= \left( \begin{array}{ccc} 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 \end{array} \right) $,and according to this question:Use a parity check matrix for Ham(4,2) and syndrome decoding .The syndrome decoding is the $y_1H^T$,and the Nth bit have to switch ,$1 \to 0$ or $0 \to 1$.
However,my result of $y_1H^T$ is $1110$,that is,the $14th$ bit in the $y_1$ have to switch ,but i have only $8$ bits in here,what do i do?or where am i wrong?
You need to change the first bit of $y_1$ since this column is the transpose of $1110$. So $10010110$ is a code word.
Note that in this example, in contrast to the other problem you reference, the columns do not form the binary representations of $1,2,3,...$