Constructing of 16x16 Involutory Binary Matrices of Branch Number 7

Question

In the PDF “Algebraic Construction of 16×16 Binary Matrices of Branch Number 7 with One Fixed Point”, it was given that:

Matrix 1h = 1 0 0 0
            0 1 0 0
            0 0 1 0
            0 0 0 1

Matrix 2h = 0 0 0 1 
            1 0 0 1 
            0 1 0 0 
            0 0 1 0

Matrix 4h = 0 0 1 0
            0 0 1 1
            1 0 0 1
            0 1 0 0

Matrix Fh = 1 1 1 1
            1 0 0 0
            1 1 0 0
            1 1 1 0

What are the values of 3h, 5h, 7h, Ah, Eh?

Answer 1

I guess you can construct those matrices simply with M1h and M2h with a double and add algorithm.

Clearly, $M_{4h} = M_{2h} \cdot M_{2h}$ and $M_{Fh} = ((((M_{2h} \oplus M_{1h}) \cdot M_{2h}) \oplus M_{1h}) \cdot M_{2h}) \oplus M_{1h} $. From this you can deduce how to construct all the remaining matrices.