## 80 Reputation

6 years, 166 days

## How to find k-th root of the given matri...

Maple

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).

## How to find roots of polynomial in finit...

Maple

Hi EveryOne!

I have polynomial: p(x) = x^4 + 27x^3 + x^2 + 16x +1 over finite field F=GF(2^8)/f(x)=x^8 + x^4 +x^3 +1

The factors of this polynomial are: (x + 37)(x + 217)(x^2 + 213x +30) (in maple)

Hence there two roots of p(x): x = 37 and x = 217 in GF(2^8). The factor x^2 + 231x +30 is of degree 2. There are not roots in F. But in extension field GF((2^8)^2) of F, also there are two roots of factor x^2 + 213x + 30 (for example: x = 256 and x = 256^256 = 487).

How to find these roots of p(x) in extension field GF((2^8)^2) by maple? Please help me! Thanks a lot.

## How to compute Eigenvalues and Eigenvect...

Maple

How to compute Eigenvalues and Eigenvectors of the matrix over finite field? Thank you very much

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