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Galois Field

modular polynomials GF(2²) - GF(2¹²)

111
1011
10011
100101
1000011
10001001
100011101
1000010001
10000001001
1000001010011

package testing

from GaloisField import gf

#construction of Galois Field GF(2³)
m = 3
GF = gf(m)
>>> GF(2³)

polynomial representation

GF.modPol_pr()
>>> α³ + α¹ + α⁰

vector representation

GF.modPol_vr()
>>> 1011

alpha elements

alphas = GF.getElements()
alphas
>>> [001, 010, 100, 011, 110, 111, 101]

vector representation

alphas[1]
>>> 010

polynomial representation

alphas[1].getAlpha()
>>> α¹

operations

1. addition

alphas[0] + alphas[1]
>>> 011

2. multiplication

alphas[1] * alphas[2]
>>> 011

3. inverse

- alphas[1]
>>> 101

4. division

alphas[5] / alphas[2]
>>> 011

5. exponent

alphas[2] ** 3
>>> 101

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