def __init__(self, p, n):
"""
Constructs a BCH code with the
specified parameters.
:param p: a parameter of a
binary symmetric channel,
the error probability.
:param n: length of a code.
"""
t, n, k, power = initiate(p=p, n=n)
self.t = t
self.n = n
self.k = k
self.power = power
primitive_polynomial = get_primitive_polynomial(power=power, k=1)
cyclotomic_cosets = get_cyclotomic_cosets(power=power)
logarithmic_table = build_logarithmic_table(
power=power, primitive_polynomial=primitive_polynomial)
generator_polynomial = calculate_generator_polynomial(
primitive_polynomial=primitive_polynomial,
cyclotomic_cosets=cyclotomic_cosets,
logarithmic_table=logarithmic_table,
power=power,
t=t)
self.primitive_polynomial = primitive_polynomial
self.cyclotomic_cosets = cyclotomic_cosets
self.logarithmic_table = logarithmic_table
self.generator_polynomial = generator_polynomial
print()
print("t: {0}".format(t))
print("n: {0}".format(n))
print("k: {0}".format(k))
print("Generator polynomial: {0:b}".format(generator_polynomial))
def test_decode(self):
power = 4
t = 2
primitive_polynomial = 0b10011
cyclotomic_cosets = get_cyclotomic_cosets(power=power)
logarithmic_table = build_logarithmic_table(
power=power, primitive_polynomial=primitive_polynomial)
generator_polynomial = calculate_generator_polynomial(
primitive_polynomial=primitive_polynomial,
cyclotomic_cosets=cyclotomic_cosets,
logarithmic_table=logarithmic_table,
power=power,
t=t)
count = 0
for i in range(10):
error_vector = get_random_number_of_hamming_weight(
length=2**power - 1, weight=t)
for message in range(2**(2**power - 1 - power * t)):
codeword = encode(generator_polynomial=generator_polynomial,
message=message,
power=power,
t=t)
received_message = codeword ^ error_vector
decoded = decode(primitive_polynomial=primitive_polynomial,
received_message=received_message,
cyclotomic_cosets=cyclotomic_cosets,
logarithmic_table=logarithmic_table,
power=power,
t=t)
if decoded != message:
count += 1
assert count == 0
def test_get_cyclotomic_cosets(self):
power = 8
result = 0
counter = 0
for i in get_cyclotomic_cosets(power=power):
result ^= i
counter += 1
result ^= 1
assert result == 2 ** (2 ** power - 1) - 1
assert counter >= power
def test_calculate_generator_polynomial(self):
primitive_polynomial = get_primitive_polynomial(power=self.power, k=1)
cyclotomic_cosets = get_cyclotomic_cosets(power=self.power)
logarithmic_table = build_logarithmic_table(
power=self.power, primitive_polynomial=primitive_polynomial)
generator_polynomial = calculate_generator_polynomial(
primitive_polynomial=primitive_polynomial,
cyclotomic_cosets=cyclotomic_cosets,
logarithmic_table=logarithmic_table,
power=self.power,
t=self.t)
assert generator_polynomial == 0b111010001
def test_get_syndromes(self):
power = 5
t = 3
primitive_polynomial = 0b100101
received_message = 0b100101000000001
cyclotomic_cosets = get_cyclotomic_cosets(power=power)
logarithmic_table = build_logarithmic_table(
power=power, primitive_polynomial=primitive_polynomial)
syndromes = get_syndromes(primitive_polynomial=primitive_polynomial,
received_message=received_message,
cyclotomic_cosets=cyclotomic_cosets,
logarithmic_table=logarithmic_table,
power=power,
t=t)
assert syndromes == [0, 0, 29, 0, 23, 27]
def test_berlekamp_massey_decode(self):
power = 4
t = 2
primitive_polynomial = 0b10011
received_message = 0b000011001100011
cyclotomic_cosets = get_cyclotomic_cosets(power=power)
logarithmic_table = build_logarithmic_table(
power=power, primitive_polynomial=primitive_polynomial)
syndromes = get_syndromes(primitive_polynomial=primitive_polynomial,
received_message=received_message,
cyclotomic_cosets=cyclotomic_cosets,
logarithmic_table=logarithmic_table,
power=power,
t=t)
assert berlekamp_massey_decode(syndromes=syndromes,
logarithmic_table=logarithmic_table,
power=power,
t=t) == [0, 2, 14, -1, -1]
def test_get_polynomial_from_roots(self):
power = 4
assert get_polynomial_from_roots(
roots=get_cyclotomic_cosets(power)[1],
power=power,
logarithmic_table=build_logarithmic_table(power, 0b10011)) == 0b11111