Minimal polynomials - PowerPoint PPT Presentation

Minimal Polynomials

Minimal Polynomials. The minimal polynomial of element  of is the monic polynomial h(x) of least degree in GF p [x] such that h() = 0 when evaluated in Notation: the minimal polynomial of  is denoted m  (x). Minimal Polynomials.

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Finite Fields

Finite Fields. Rong-Jaye Chen. Finite fields. 1. Irreducible polynomial f(x) K[x], f(x) has no proper divisors in K[x] Eg. f(x)=1+x+x 2 is irreducible f(x)=1+x+x 2 +x 3 =(1+x)(1+x 2 ) is not irreducible f(x)=1+x+x 4 is irreducible. Finite fields. 2. Primitive polynomial

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