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| how to quickly find ONE primitive polynomial in GF(2^m) https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1828 |
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| Author: | gepo [ Fri Apr 30, 2010 3:45 am ] |
| Post subject: | how to quickly find ONE primitive polynomial in GF(2^m) |
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 |
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| Author: | gorzel [ Mon May 03, 2010 6:42 pm ] |
| Post subject: | Re: how to quickly find ONE primitive polynomial in GF(2^m) |
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 |
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