def shiftSyndrome(self, S, i = 1):
"""Shift syndrome i times (slide 35)
"""
for i in range(0, i):
# S1(X) = XS(X) mod g(X)
S = GF2.modPoly(GF2.multPoly(X(1), S), self.g())
return S
def shiftSyndrome(self, S, i=1):
"""Shift syndrome i times (slide 35)
"""
for i in range(0, i):
# S1(X) = XS(X) mod g(X)
S = GF2.modPoly(GF2.multPoly(X(1), S), self.g())
return S
def shift(self, c, i = 1):
"""Cyclic right shift of c using division (slide 11)
"""
Xi = X(i) # X^i polynomial
XiCX = GF2.multPoly(Xi, c) # X^i * c(X) polynomial
Xn1 = GF2.addPoly(X(self.n()), X(0)) # X^n + 1 polynomial
ci = GF2.modPoly(XiCX, Xn1) # i times shifted c
return padEnd(ci, self.n())
def shift(self, c, i=1):
"""Cyclic right shift of c using division (slide 11)
"""
Xi = X(i) # X^i polynomial
XiCX = GF2.multPoly(Xi, c) # X^i * c(X) polynomial
Xn1 = GF2.addPoly(X(self.n()), X(0)) # X^n + 1 polynomial
ci = GF2.modPoly(XiCX, Xn1) # i times shifted c
return padEnd(ci, self.n())
def printMessageCodewordTable(self, systematic = True): # override
"""Print all messages and their corresponding codewords.
Args:
systematic: print codewords in systematic form (default: True)
"""
M = self.M()
print('Messages -> Codewords')
for m in M:
c = self.c(m, systematic)
print(m, c, 'm(X) =', GF2.polyToString(m), '\tc(X) =', GF2.polyToString(c) )
def encode(m, g, systematic = True):
if systematic:
r = degree(g) # r = n - k
Xr = X(r) # X^(n-k)
XrmX = GF2.multPoly(Xr, m) # X^(n-k) * m(X)
p = GF2.modPoly(XrmX, g) # p(X) = (X^(n-k) * m(X)) mod g(X)
c = GF2.addPoly(p, XrmX) # c(X) = p(X) + (X^(n-k) * m(X))
else:
c = GF2.multPoly(m, g)
return c.astype(int)
def printMessageCodewordTable(self, systematic = True): # override
"""
Print all messages and their corresponding codewords.
Args:
systematic: print codewords in systematic form (default: True)
"""
M = self.M()
print('Messages -> Codewords')
for m in M:
c = self.c(m, systematic)
print(m, c, 'm(X) =', GF2.polyToString(m), '\tc(X) =', GF2.polyToString(c) )
def encode(m, g, systematic = True):
"""Encoding of cyclic code (in systematic form)
(slide 23)
ATTENTION: Dangling zeros in returned codeword are cut away.
"""
if systematic:
r = degree(g) # r = n - k
Xr = X(r) # X^(n-k)
XrmX = GF2.multPoly(Xr, m) # X^(n-k) * m(X)
p = GF2.modPoly(XrmX, g) # p(X) = (X^(n-k) * m(X)) mod g(X)
c = GF2.addPoly(p, XrmX) # c(X) = p(X) + (X^(n-k) * m(X))
else:
c = GF2.multPoly(m, g)
return c.astype(int)
def encode(m, g, systematic=True):
"""Encoding of cyclic code (in systematic form)
(slide 23)
ATTENTION: Dangling zeros in returned codeword are cut away.
"""
if systematic:
r = degree(g) # r = n - k
Xr = X(r) # X^(n-k)
XrmX = GF2.multPoly(Xr, m) # X^(n-k) * m(X)
p = GF2.modPoly(XrmX, g) # p(X) = (X^(n-k) * m(X)) mod g(X)
c = GF2.addPoly(p, XrmX) # c(X) = p(X) + (X^(n-k) * m(X))
else:
c = GF2.multPoly(m, g)
return c.astype(int)
def S(self, r):
"""Calculate Syndrome polynomial from receive or error polynomial.
Args:
r: receive or error polynomial
Returns:
Syndrome polynomial
"""
return GF2.modPoly(r, self.g())
def S(self, r):
"""Calculate Syndrome polynomial from receive or error polynomial.
Args:
r: receive or error polynomial
Returns:
Syndrome polynomial
"""
return GF2.modPoly(r, self.g())
def dmin(self, verbose = False): # override (LinearBlockCode dmin would work, but is slower)
dmin = lbc.w(self.g())
if verbose:
print()
print('Minimum Hamming distance (d_min) equals weight of generator polynomial g(X):')
print('g(X) =', GF2.polyToString(self.g()))
print('d_min =', dmin)
print()
return dmin
def exam2011problem3():
G = np.array([[1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0],
[0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0],
[0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1]])
g = np.array([1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1])
X15 = np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1])
print(GF2.polyToString(GF2.divPoly(X15, g)))
G = cyccode.makeSystematic(G, True)
lbc = LinearBlockCode()
lbc.setG(G)
r = np.array([1, 0, 1, 1, 0])
c = lbc.c(r)
print(c)
def dmin(self, verbose = False): # override
#(LinearBlockCode dmin would work, but is slower)
dmin = lbc.w(self.g())
if verbose:
print()
print('Minimum Hamming distance (d_min) equals weight of generator polynomial g(X):')
print('g(X) =', GF2.polyToString(self.g()))
print('d_min =', dmin)
print()
return dmin
def printAllCyclicCodes(factorPolynomials):#выводим все циклические коды, которые можем сделать
s = ''
product = np.array([])
for i in range(0, len(factorPolynomials)):
if i == 0:
product = factorPolynomials[i]
else:
product = GF2.multPoly(product, factorPolynomials[i])
s += '(' + GF2.polyToString(factorPolynomials[i]) + ') '
print(s + '= ' + GF2.polyToString(product))
print()
numberCodes = 2**(len(factorPolynomials)) - 2
n = degree(product)
print('Всего возможны', numberCodes, 'различных циклических кодов длиной', n)
print('так как мы можем найти', numberCodes, 'различных неприводимых двоичных полиномов')
print(GF2.polyToString(product))
print(np.bitwise_and(1, 3))
print('Code <- Generator polynomial')
for i in range(0, numberCodes):
s = ''
gp = np.array([]) # generator polynomial
for j in range(0, len(factorPolynomials)):
if np.bitwise_and(i+1, 2**j) > 0:
if s =='':
gp = factorPolynomials[j]
else:
gp = GF2.multPoly(gp, factorPolynomials[j])
s += '(' + GF2.polyToString(factorPolynomials[j]) + ')'
print('Ccyc(' + str(n) + ', ' + str(degree(gp)) + ') <- g' + str(i+1) + ' = ' + s + ' = ' + GF2.polyToString(gp))
def printAllCyclicCodes(factorPolynomials):
"""Generates all cyclic codes that can be created from
the given factor polynomials.
(slide 28)
Args:
factorPolynomials: factor polynomials in a python array
"""
s = ''
product = np.array([])
for i in range(0, len(factorPolynomials)):
if i == 0:
product = factorPolynomials[i]
else:
product = GF2.multPoly(product, factorPolynomials[i])
s += '(' + GF2.polyToString(factorPolynomials[i]) + ') '
print(s + '= ' + GF2.polyToString(product))
print()
numberCodes = 2**(len(factorPolynomials)) - 2
n = degree(product)
print('There are', numberCodes, 'different cyclic codes of length', n,
'as')
print('we can find', numberCodes,
'different generator polynomials that are')
print('the factors of', GF2.polyToString(product))
print(np.bitwise_and(1, 3))
print('Code <- Generator polynomial')
for i in range(0, numberCodes):
s = ''
gp = np.array([]) # generator polynomial
for j in range(0, len(factorPolynomials)):
if np.bitwise_and(i + 1, 2**j) > 0:
if s == '':
gp = factorPolynomials[j]
else:
gp = GF2.multPoly(gp, factorPolynomials[j])
s += '(' + GF2.polyToString(factorPolynomials[j]) + ')'
print('Ccyc(' + str(n) + ', ' + str(degree(gp)) + ') <- g' +
str(i + 1) + ' = ' + s + ' = ' + GF2.polyToString(gp))
def printAllCyclicCodes(factorPolynomials):
"""Generates all cyclic codes that can be created from
the given factor polynomials.
(slide 28)
Args:
factorPolynomials: factor polynomials in a python array
"""
s = ''
product = np.array([])
for i in range(0, len(factorPolynomials)):
if i == 0:
product = factorPolynomials[i]
else:
product = GF2.multPoly(product, factorPolynomials[i])
s += '(' + GF2.polyToString(factorPolynomials[i]) + ') '
print(s + '= ' + GF2.polyToString(product))
print()
numberCodes = 2**(len(factorPolynomials)) - 2
n = degree(product)
print('There are', numberCodes, 'different cyclic codes of length', n, 'as')
print('we can find', numberCodes, 'different generator polynomials that are')
print('the factors of', GF2.polyToString(product))
print(np.bitwise_and(1, 3))
print('Code <- Generator polynomial')
for i in range(0, numberCodes):
s = ''
gp = np.array([]) # generator polynomial
for j in range(0, len(factorPolynomials)):
if np.bitwise_and(i+1, 2**j) > 0:
if s =='':
gp = factorPolynomials[j]
else:
gp = GF2.multPoly(gp, factorPolynomials[j])
s += '(' + GF2.polyToString(factorPolynomials[j]) + ')'
print('Ccyc(' + str(n) + ', ' + str(degree(gp)) + ') <- g' + str(i+1) + ' = ' + s + ' = ' + GF2.polyToString(gp))
def printg(self):
print(GF2.polyToString(self.g()))
def exam2014problem3():
g1 = np.array([1, 0, 0, 1])
g2 = np.array([1, 1, 1, 1])
r, t = GF2.HCF(g1, g2, True)
print(GF2.polyToString(t))
def printg(self):
print(GF2.polyToString(self.g()))