How do I compute a level-four Hankel matrix ?

Hello everyone, I am trying to embed a 4-D spatial hypercube Dk1, k2, k3, k4 in a level-four block Hankel matrix as follows. I need to first embed the data in a level-one Hankel matrix using all data components in the first dimension of the tensor Dk1,k2,k3,k4 at a given frequency w0. I have to addressed in advance that each frequency slice of data is operated the exactly same way. I need to operate in the following way :

• first, embed the data in a level-one Hankel matrix using all data components in the first dimension of the tensor Dk1,k2,k3,k4 at a given frequency w0.
• then, these matrices are embedded gradually in a level-two, three and level-four block Hankel matrices.

The level-four is the target matrix of my problem. The size of level-four block Hankel matrix M(4) is (Y1Y2Y3Y4) × (X1 − Y1 + 1)(X2 − Y2+ 1)(X3 − Y3 + 1)(X4 − Y4 + 1). If Xi is an odd integer, the size of M(4) is (Y1Y2Y3Y4) × (Y1Y2Y3Y4).

You will find attached more detail about my concern.

I trying to compute these matrices in oder to get target matrix (level-four) but I meet a lot difficulties. I need any help that could help me to get my target.

Thanks for giving me a hand.