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binary value of an irreducible polynomial

asked 2020-05-29 15:58:38 +0200

Hassan Mostafa gravatar image

if i defined the following finite field

F=GF(2^15,'x')

then i've generated it's irreducible polynomial

sage: IP=F.polynomial()
sage: IP
x^15 + x^5 + x^4 + x^2 + 1

how can i get the binary representation of this polynomial ?

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answered 2020-05-29 16:04:39 +0200

tmonteil gravatar image

updated 2020-05-29 16:05:16 +0200

I am not completely sure about what you call binary representation of the polynomial, but i could suggest:

sage: IP.coefficients(sparse=False)
[1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]

If you want the bit of low weight to be on the right, you can do:

sage: L = IP.coefficients(sparse=False)
sage: L.reverse()
sage: L
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1]
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Asked: 2020-05-29 15:58:38 +0200

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Last updated: May 29 '20