Algorithm 1 Correct one deletion symbol.

Input:  $n,d,a,e,\mathit{y}={\mathit{c}}_j^{n-1}\in {\mathbb{F}}_4^{n-1}$. Output:  $\mathit{c}=(c_1,c_2,\dots ,c_n)\in C(n,4)$.  1:$c_j=e-{\sum }_{i=j}^{n-1}{y}_i \mathrm{mod} 4$.  2:Get the binary sequence $0{\mathit{x}}_j^{n-1}$ and the run-length vector ${\mathit{r}}^{{}^{\prime }}$ of $0{\mathit{x}}_j^{n-1}$.  3:Get the total number of elements of ${\mathit{r}}^{{}^{\prime }}$ as $\parallel {\mathit{r}}^{{}^{\prime }}\parallel$.  4:$\Delta =d-Rsyn\left(0{\mathit{x}}_j^{n-1}\right) \mathrm{mod} 2n$.  5:Set $j=1$.  6:while  $j\le n$  do  7:   if $\Delta <\parallel {\mathit{r}}^{{}^{\prime }}\parallel$ then  8:     if $k_{0{\mathit{x}}_j^{n-1}}(j-1)=\Delta$ then  9:        $\mathit{c}=$del_correct1$(n,a,\mathit{y},j,c_j)$  10:     else  11:        $j\leftarrow j+1$  12:     end if  13:   else  14:     if $k_{0{\mathit{x}}_j^{n-1}}(j-1)+2(n-j)-1=\Delta$ then  15:        $\mathit{c}=$del_correct1 $(n,a,\mathit{y},j,c_j)$  16:     else  17:        $j\leftarrow j+1$  18:     end if  19:   end if  20:end while