##  [Berlekamp Algorithm](/berlekamp-algorithm) 

  ##  [Berlekamp Algorithm](https://algebra.quantumdictionary.io/berlekamp-algorithm-0) 

  

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Definition

An algorithm to factor polynomials over finite fields that uses linear algebra to find the Berlekamp subalgebra: one computes a basis of polynomials fixed by the Frobenius map (x → x^q) modulo the polynomial and extracts nontrivial factors via gcds with linear combinations of basis elements.