Il giorno Fri, 5 Dec 2008 22:06:40 +0100 [EMAIL PROTECTED] ha scritto: > As the Galois field is represented as a set on "int" values the > maximum Galois feild that can be represented is GF(2^31), which was a > primitive polynomial of order 32. This is in fact the "grade" I was > talking about.
Ok. But this is clearly enough for me!I'm trying to generate a GF(2^18) or a GF(2^20), I don't need a polynomial of order higher than 20 to do so. > It seems the grade you are talking about is the order > of the BCH generator polynomial, which is constructed from the > cyclotomic cosets of the galois field (cf the cosets function). I'd > have to look up the exact process to construct the BCH generator > polynomial from the cosets, but if I remember correctly the order of > the BCH generator polynomial is always less that the order of the > primitive polynomial of the galois field, and so yes the limit on the > order or "grade" of the BCH generator polynomial in the octave-foreg > package is 31.. Have you looked at the PARI/GP package that might be > what you are looking for to work with such large generator > polynomials? Check > > http://pari.math.u-bordeaux.fr/ > > Regards > David I know that, in fact my problem is that I'm not overstepping the limit. However you don't remember well, there's not a strict relationship between the order of the primitive and the order of the generator. In fact to obtain a generator you have to multiply a set of minimal polynomials and among them there could be the primitive but not necessarily. The grade of the generator can be very high even if grade of the primitive is low and the reason is that, as you surely know, the grade of the generator is related to the redundance added to the word, that are the parity bits, i.e. in BCH(511,10) the generator has grade 501 and the primitive has grade 9 (2^9 = 512). When I say GRADE I don't mean the order, I mean the greatest n in this polynomial: x^n + x^(n-1) + ...+ x + 1 This polynomial has grade n. As I know in coding theory this is not necessarily its order. So it seems that my problem is not related to CPU architecture but to the Octave code, that's why I asked help. Thanks to your previous advice now I don't have the limit on the grade of the primitive set to 16 anymore but I receive the other error. I paste my problem again to make it easier for you: >> I have made some tests. Now when I try to create a BCH code with >> n=262128 and k=261960, with a generator polyonomial of grade 168 I >> receive: >> >> error: primitive polynomial (0) of Galois Field must be irreducible >> error: unable to initialize Galois Field >> Please note that n=262128 can be obtained with a primitive polynomial of grade 18 (n^18=262144) so we are far from GF(31) or GF(63) limit... The grade of the generator is 168 as n-k=168 (so again its grade is bigger than the primitive's). Thanks again Marco -- Per favore non mandatemi allegati in Word o PowerPoint. Si veda http://www.gnu.org/philosophy/no-word-attachments.html
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