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Question: How to find k-th root of the given matrix over finite field

Question:How to find k-th root of the given matrix over finite field

testht06 90 Maple
matrix homework eigenvalues finite-field
April 16 2015
1

Hi EveryOne!

In the the answer of the question "How to find roót of polynomial in finite field and extension finite field (at URL: http://www.mapleprimes.com/questions/203977-How-To-Find-Roots-Of-Polynomial-In-Finite#answer215097). Carl Love helped compute eigenvalues (x1,x2,...,xn)and eigenvectors of the given matrix M over GF(28)/(y^8+y^4+y^3+y+1).

I need to do:

1. Get matrix D from these eigenvalues (x1,x2,...,xn), with D[i,i] = xi and D[i,j≠i] = 0 (D will be diagonalizable matrix. Some xi may be in extension finite field  GF((28)2))

2. Get matrix P from eigenvectors corresponding to the above eigenvalues, compute P-1

3. Compute matrix B = P x D1/4 x P-1 in  extension finite field  GF((28)2).

Please help me!!! 
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