how to quickly find ONE primitive polynomial in GF(2^m)

gepo · Fri Apr 30, 2010 3:45 am

Hi,
How to quickly find ONE primitive polynomial in GF(2^m) with "m" up to 2048 ?
I have searched for a while but failed to find such a function.

Thanks
Gepo

Re: how to quickly find ONE primitive polynomial in GF(2^m)

gorzel · Mon May 03, 2010 6:42 pm

gepo wrote:

Hi,
How to quickly find ONE primitive polynomial in GF(2^m) with "m" up to 2048 ?
I have searched for a while but failed to find such a function.

Thanks
Gepo

Supposed you mean: GF(2^m) with 2^m<= 2048 (and not m<=2048)
you can define in Singular theses Galois fields and then display the minimal polynomial.

Code:

ring r2048 = (2^11,a),x,dp;
minpoly;

It is unlikly that an explicit function for the minpolys exist. But on
Frank Luebeck's website you find lists of primitive polynomials and
two methods how to compute the Conway polynomials:

http://www.math.rwth-aachen.de/~Frank.L ... index.html

C. Gorzel