Encoding a polar code

The recursive $\left(U+V\mid V\right)$ structure of a polar code leads in a natural way to an encoding algorithm for it. We use the following algorithm to encode a polar code. To encode a polar code of length $2^n$ and dimension $k$ we take a binary vector $\mathbf{u}$ with $2^n-k$ positions fixed to 0 and $k$ positions where the information bits are copied to. Encoding is performed by calling Encode $(0,2^n,n,\mathbf{u})$ and by outputting the resulting vector $\mathbf{u}$.

Implement this function in Java and check that it gives the right encoding of the polar code of length $8$ that you have found in the previous question.