Algorithm 3$f_X(V_X,D)$: Encoding a value with subroutines $X_G$ and $X_L$

Input: Value to be encoded $V_X$, vector size D Ensure: $V_X\in R$ and $D\ge 3$ Output: Array of vectors $\left[{\mathbf{x}}_{0,L},{\mathbf{x}}_{0,G},{\mathbf{x}}_{1,L},{\mathbf{x}}_{1,G},\dots ,{\mathbf{x}}_{D-3,L},{\mathbf{x}}_{D-3,G}\right]$ 1:$N\leftarrow D-2$ {Number of vectors} 2:$i\leftarrow D-2$ {Highest power of 2} 3:$n\leftarrow 0$ {Current vector} 4:while$n<N$do {$0\le n<N$} 5: if $V_X\ge 2^i$ then 6:  ${\mathbf{x}}_{n,L}\leftarrow X_L(2^i,D)$ 7:  ${\mathbf{x}}_{n,R}\leftarrow X_G(2^i,D)$ 8:  $n\leftarrow n+1$ 9:  $V_X\leftarrow V_X-2^i$ 10: else if $V_X=0$ then 11:  ${\mathbf{x}}_{n,L}\leftarrow X_L(0,D)$ 12:  ${\mathbf{x}}_{n,R}\leftarrow X_G(0,D)$ 13:  $n\leftarrow n+1$ 14: else 15:  $i\leftarrow i-1$ 16: end if 17: end while 18: return $\left[{\mathbf{x}}_{0,L},{\mathbf{x}}_{0,G},{\mathbf{x}}_{1,L},{\mathbf{x}}_{1,G},\dots ,{\mathbf{x}}_{N-1,L},{\mathbf{x}}_{N-1,G}\right]$