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Question: a nullspace example in relation with Berlekamp

Question: a nullspace example in relation with Berlekamp

Blanc 15 Maple 2023
modular linearalgebra linear-algebra nullspace incomplete-question
February 17 2025
0

 

Hello,

I tried to apply Berlekamp's theory to the polynomial X^9+X^6-X+1 in F3.
The matrix of the linear application whose kernel dimension is sought is:

 The dimension should be equal to 2 according to the theory since this polynomial decomposes into 2 irreducible polynomials.
However, the nullspace instruction of maple does not give a result consistent with the theory. Please help me find what is happening.

 
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