Algorithm A1 Correct one insertion symbol

Input:  $n,a,\mathit{y},0{\mathit{x}}_j^{n+1}$. Output:  $\mathit{c}=(c_1,c_2,\dots ,c_n)\in C(n,4)$.  1:Calculate $\Delta$ and $h_1$ as in Table 3.  2:Set $j=1$.  3:while  $j\le n+1$ do  4:   if $\Delta <\parallel {\mathit{r}}^{{}^{\prime }}\parallel$ then  5:     if $\mathrm{mod}(\Delta ,2)=1$ then  6:        if $k_{0{\mathit{x}}_j^{n+1}}(j-1)+1=\Delta$ then  7:          $\mathit{c}=$ins1_correct1$(n,a,\mathit{y},j,h_1)$  8:        else  9:          $j\leftarrow j+1$  10:        end if  11:     else  12:        if $k_{0{\mathit{x}}_j^{n+1}}(j-1)=\Delta$ then  13:          $\mathit{c}=$ins1_correct1$(n,a,\mathit{y},j,h_1)$  14:        else  15:          $j\leftarrow j+1$  16:        end if  17:     end if  18:   else  19:     if $k_{0{\mathit{x}}_j^{n+1}}(j-1)+2(n-j+1)+1=\Delta$ then  20:        $\mathit{c}=$ins1_correct1$(n,a,\mathit{y},j,h_1)$  21:     else  22:        $j\leftarrow j+1$  23:     end if  24:   end if  25:end while