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Is there an easy way to calculate irreducible polynomials in GF(2^n) or is it more practical to just memorize them?

I hate memorizing this stuff just as much as the next person but I can't figure out a fast way to get them that doesn't involve multiple divisions that take way too long.

Shiroyasha
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    Depends on many things. For one, are you talking about irreducible polynomials with coefficients in $GF(2^n)$, or about degree $n$ irreducible polynomials with coefficients in $GF(2)$ (we typically use one such to construct the bigger field)? If the former, I wouldn't bother memorizing. If the latter... depends on $n$ :-) I have memorized all of them up to degree $4$, and at least one of degree $5$ to $8$. From that point on I resort to a table listing, say, a lowest weight primitive polynomial. Anyway, memorizing irreducible polynomials with coefficients in a prime field is at par with – Jyrki Lahtonen Mar 11 '18 at 19:45
  • (cont'd) memorizing tables of prime numbers. In other words, not very useful in general, but there are those that you encounter so frequently that you remember them a bit like you remember an acquaintance from a hobby group :-) – Jyrki Lahtonen Mar 11 '18 at 19:47
  • Also, if you remember one, there are tricks for producing more. – Jyrki Lahtonen Mar 11 '18 at 19:49

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