def gen_m_sequence(taps, init=0x2):
degree = utils.get_highest_set_bit(taps)
mask = (2 ** (1+degree)) - 1
bins = init
done = 0
output = []
while not done:
output.append(1 if bins & 1 else 0)
bins = ((bins >> 1) +
((utils.count_bits(taps & bins) % 2) << (degree-1))) & mask
if bins == init or bins == 0:
done = 1
return numpy.array(output)
def get_primitive_polys_gf2(deg, max_num=None, random=True):
# From http://www.seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/theory.html
# Step 1: Generate a polynomial
r = (2 ** deg) - 1
ret = []
for poly in xrange(1 << deg, 1 << (deg + 1)):
# Step 2 (not needed for GF2)
# Step 3: check f(a)!=0 for 1 <= a <= p-1
if (utils.count_bits(poly) % 2) == 0:
continue
# Step 4:
if not berlekamp_factorisation_check(poly):
continue
# Step 5: x**r == a(mod f(x), p) for some integer a (gf(2) means a == 1)
if utils.gf2_mod(1 << r, poly) != 1:
continue
# Step 6: skip
# Step 7:
p_k = list(set(utils.find_prime_factors(r)))
passed = True
for p in p_k:
if utils.gf2_mod(1 << (r/p), poly) == 1:
passed = False
if not passed:
continue
#print poly
ret.append(poly)
print "Found poly = " + bin(poly)
if max_num and len(ret) >= max_num:
return ret
return ret
