def test_closure(self):
for m in arange(1, 9):
x = GF(arange(2**m), m)
for a in x.elements:
for b in x.elements:
assert_((GF(array([a]), m) +
GF(array([b]), m)).elements[0] in x.elements)
assert_((GF(array([a]), m) *
GF(array([b]), m)).elements[0] in x.elements)
def test_minpols(self):
m = 4
x = GF(arange(2**m), m)
z = array([2, 3, 19, 19, 19, 19, 7, 7, 31, 25, 31, 25, 31, 25, 25, 31])
assert_array_equal(x.minpolys(), z)
m = 6
x = GF(array([2, 8, 32, 6, 24, 35, 10, 40, 59, 41, 14, 37]), m)
z = array([67, 87, 103, 73, 13, 109, 91, 117, 7, 115, 11, 97])
assert_array_equal(x.minpolys(), z)
def test_power_form(self):
m = 3
x = GF(arange(1, 2**m), m)
y = x.tuple_to_power()
z = GF(array([0, 1, 3, 2, 6, 4, 5]), m)
assert_array_equal(y.elements, z.elements)
m = 4
x = GF(arange(1, 2**m), m)
y = x.tuple_to_power()
z = GF(array([0, 1, 4, 2, 8, 5, 10, 3, 14, 9, 7, 6, 13, 11, 12]), m)
assert_array_equal(y.elements, z.elements)
def test_power_form(self):
m = 3
x = GF(arange(1, 2**m), m)
y = x.tuple_to_power()
z = GF(array([0, 1, 3, 2, 6, 4, 5]), m)
assert_array_equal(y.elements, z.elements)
m = 4
x = GF(arange(1, 2**m), m)
y = x.tuple_to_power()
z = GF(array([0, 1, 4, 2, 8, 5, 10, 3, 14, 9, 7, 6, 13, 11, 12]), m)
assert_array_equal(y.elements, z.elements)
def test_minpols(self):
m = 4
x = GF(arange(2**m), m)
z = array([2, 3, 19, 19, 19, 19, 7, 7, 31, 25, 31, 25, 31, 25, 25, 31])
assert_array_equal(x.minpolys(), z)
m = 6
x = GF(array([2, 8, 32, 6, 24, 35, 10, 40, 59, 41, 14, 37]), m)
z = array([67, 87, 103, 73, 13, 109, 91, 117, 7, 115, 11, 97])
assert_array_equal(x.minpolys(), z)
def cyclic_code_genpoly(n, k):
"""
Generate all possible generator polynomials for a (n, k)-cyclic code.
Parameters
----------
n : int
Code blocklength of the cyclic code.
k : int
Information blocklength of the cyclic code.
Returns
-------
poly_list : 1D ndarray of ints
A list of generator polynomials (represented as integers) for the (n, k)-cyclic code.
"""
if n % 2 == 0:
raise ValueError("n cannot be an even number")
for m in arange(1, 18):
if (2**m - 1) % n == 0:
break
x_gf = GF(arange(1, 2**m), m)
coset_fields = x_gf.cosets()
coset_leaders = array([])
minpol_degrees = array([])
for field in coset_fields:
coset_leaders = concatenate(
(coset_leaders, array([field.elements[0]])))
minpol_degrees = concatenate(
(minpol_degrees, array([len(field.elements)])))
y_gf = GF(coset_leaders, m)
minpol_list = y_gf.minpolys()
idx_list = arange(1, len(minpol_list))
poly_list = array([])
for i in range(1, 2**len(minpol_list)):
i_array = dec2bitarray(i, len(minpol_list))
subset_array = minpol_degrees[i_array == 1]
if int(subset_array.sum()) == (n - k):
poly_set = minpol_list[i_array == 1]
gpoly = 1
for poly in poly_set:
gpoly_array = dec2bitarray(gpoly, 2**m)
poly_array = dec2bitarray(poly, 2**m)
gpoly = bitarray2dec(convolve(gpoly_array, poly_array) % 2)
poly_list = concatenate((poly_list, array([gpoly])))
return poly_list.astype(int)
def test_order(self):
m = 4
x = GF(arange(1, 2**m), m)
y = x.order()
z = array([1, 15, 15, 15, 15, 3, 3, 5, 15, 5, 15, 5, 15, 15, 5])
assert_array_equal(y, z)
def test_tuple_form(self):
m = 3
x = GF(arange(0, 2**m-1), m)
y = x.power_to_tuple()
z = GF(array([1, 2, 4, 3, 6, 7, 5]), m)
assert_array_equal(y.elements, z.elements)
def test_order(self):
m = 4
x = GF(arange(1, 2**m), m)
y = x.order()
z = array([1, 15, 15, 15, 15, 3, 3, 5, 15, 5, 15, 5, 15, 15, 5])
assert_array_equal(y, z)
def test_tuple_form(self):
m = 3
x = GF(arange(0, 2**m - 1), m)
y = x.power_to_tuple()
z = GF(array([1, 2, 4, 3, 6, 7, 5]), m)
assert_array_equal(y.elements, z.elements)
def test_multiplication(self):
m = 3
x = GF(array([7, 6, 5, 4, 3, 2, 1, 0]), m)
y = GF(array([6, 4, 3, 1, 2, 0, 5, 7]), m)
z = GF(array([4, 5, 4, 4, 6, 0, 5, 0]), m)
assert_array_equal((x * y).elements, z.elements)
def test_addition(self):
m = 3
x = GF(arange(2**m), m)
y = GF(array([6, 4, 3, 1, 2, 0, 5, 7]), m)
z = GF(array([6, 5, 1, 2, 6, 5, 3, 0]), m)
assert_array_equal((x + y).elements, z.elements)
def cyclic_code_genpoly(n, k):
"""
Generate all possible generator polynomials for a (n, k)-cyclic code.
Parameters
----------
n : int
Code blocklength of the cyclic code.
k : int
Information blocklength of the cyclic code.
Returns
-------
poly_list : 1D ndarray of ints
A list of generator polynomials (represented as integers) for the (n, k)-cyclic code.
"""
if n%2 == 0:
raise ValueError("n cannot be an even number")
for m in arange(1, 18):
if (2**m-1)%n == 0:
break
x_gf = GF(arange(1, 2**m), m)
coset_fields = x_gf.cosets()
coset_leaders = array([])
minpol_degrees = array([])
for field in coset_fields:
coset_leaders = concatenate((coset_leaders, array([field.elements[0]])))
minpol_degrees = concatenate((minpol_degrees, array([len(field.elements)])))
y_gf = GF(coset_leaders, m)
minpol_list = y_gf.minpolys()
idx_list = arange(1, len(minpol_list))
poly_list = array([])
for i in range(1, 2**len(minpol_list)):
i_array = dec2bitarray(i, len(minpol_list))
subset_array = minpol_degrees[i_array == 1]
if int(subset_array.sum()) == (n-k):
poly_set = minpol_list[i_array == 1]
gpoly = 1
for poly in poly_set:
gpoly_array = dec2bitarray(gpoly, 2**m)
poly_array = dec2bitarray(poly, 2**m)
gpoly = bitarray2dec(convolve(gpoly_array, poly_array) % 2)
poly_list = concatenate((poly_list, array([gpoly])))
return poly_list.astype(int)