gf(2) Square-free factorization (sff)
Find and remove all squared factors from f.
f = b0000000000000000000000000000000000000000000000000001010000010101
f = 0x0000000000001415
f = x12 + x10 + x4 + x2 + 1
Find the derivative of f (f')
f' = b0000000000000000000000000000000000000000000000000000000000000000
f' = 0x0000000000000000
f' = 0
Since f' equals zero, find sqrt(f)
sqrt(f) = b0000000000000000000000000000000000000000000000000000000001100111
sqrt(f) = 0x0000000000000067
sqrt(f) = x6 + x5 + x2 + x + 1
In case sqrt(f) also has square factors...
Result (f factored into square-free factors)
f = (b0000000000000000000000000000000000000000000000000000000001100111)2
f = (0x0000000000000067)2
f = (x6 + x5 + x2 + x + 1)2
See also: