True is diagonal
I will again post question
Let q=28 , F = GF(28)/(t^8 + t ^4 + t^3 + t +1), square Matrix M over F (4 x 4 or 8 x 8 matrix ...)
Need to do the following tasks:
1. Compute the characteristic polynomial p(t) of the M
2. Find the factors of p(t)
3. Find the roots of these factors in the extension field of GF(q)
p(t) = (t - x1)(t-x2)...(t - xn) , where xi is the eigenvalue of M in GF(qm), where m is the maximum degree of the factor
– If a factor is of degree 1, then there is a root in GF(28), which is the constant part of the factor.
– Else the roots are 256, 256256, 256512 · · · 256256×(di−1) in GF(2(8×di))/GF(28), where di is the degree of the factor.
4. Compute eigenvectors of M and receive matrix P (each columm of P is a eigenvector corresponding to the eigenvalue xi) in GF(qm).
5. Compute P-1
6. Construct matrix diagonal D, in which D[i,i] = xi and D[i,j≠j] = 0
7. Compute D1/k (with any k as variable)
8. Compute S = P x D1/k x P-1
Please help me!