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I am running a simulation on my computer. I tried to multiply two polynomials $g(x), h(x)\in GF(2)[x]$, with $degree(g(x))= 8165$, and $degree(h(x))=25$. This multiplication took almost $20$ minutes on my computer.

Now, I have to multiply all $h(x)\in GF(2)[x]$ of $degree(h(x))\leq 25$ with $g(x)$. I estimated that it would take $2553.6$ years to complete the job. So, I would not be able to get my result in my lifetime. So, I am looking for your suggestion. Can a supercomputer finish this job in 1-4 weeks?

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    $\begingroup$ 20 minutes seems way too much, GF[2] arithmetic is so simple ! What did you use ? $\endgroup$
    – user16034
    Nov 4, 2022 at 9:23
  • $\begingroup$ By the way, what is the use of computing those 67108864 polynomials ? $\endgroup$
    – user16034
    Nov 4, 2022 at 9:24
  • $\begingroup$ With well optimized software using bit packing, I would expect below two hours of work. Maybe less with AVX vectorization. $\endgroup$
    – user16034
    Nov 4, 2022 at 9:34
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    $\begingroup$ Grrrr, wasn't I clear enough that this software is bad ? Your whole computation can be performed in an hour. $\endgroup$
    – user16034
    Nov 4, 2022 at 10:53
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    $\begingroup$ Why not, that's an option. $\endgroup$
    – user16034
    Nov 4, 2022 at 11:32

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