Re: Primitive polynomials over GF(2^m)

Derek Holt wrote:

A primitive polynomial is an irreducible polynomial of degree m with
the added constraint that the smallest integer n for which P(x)
divides X^n + 1 is n = 2^m - 1. ..(1)
...
I don't agree! The usual definition is that a primitive polynomial is
one whose roots are generators of the multiplicative group of the
extension field, and the definition given above is equivalent to that.

Except it should be x^n - 1, I guess ...

Same thing in characteristic 2, but I agree it would be preferable to
write x^n-1.

Sorry, didn't read carefully enough.
Of course the result holds in any characteristic (with p^m - 1).

Incidentally, I never realized that primitive polynomial
had another meaning: a polynomial in Z[x] with coprime coefficients.
I hope that meaning is obsolete.


.

Relevant Pages

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