def Exercise4_6():
print("Exercise4_6")
'''
A binary cyclic BCH code CBCH(n, k) has code length n = 15 and generator
polynomial g(X) = (X + 1)(1 + X + X4)(1 + X + X2 + X3 + X4).
(a) What is the minimum Hamming distance of the code?
'''
p = np.array([1, 1, 0, 0, 1])
GF16 = GaloisField(p)
#GF16.printMinimalPolynomials()
roots = GF16.conjugateRootGroups()
part1 = GF16.multPoly(GF16.minimalPolynomial(roots[1]),
GF16.minimalPolynomial(roots[2]))
part2 = GF16.multPoly(part1, GF16.minimalPolynomial(roots[3]))
print("Reduced generator polynomial: ", GF16.polyToString(part2))
print()
print(
"DMin is the number of exponents in the generator polynomial which is: ",
GF16.dminOfPoly(part2))
def Exercise4_4():
print("Exercise4_4")
'''
Determine the generator polynomial of the binary BCH code CBCH(31, 16) able
to correct error patterns of size t = 3 or less.
'''
p = np.array([1, 0, 1, 0, 0, 1])
GF25 = GaloisField(p)
GF25.printInfo()
roots = GF25.conjugateRootGroups()
print()
print("(", GF25.polyToString(GF25.minimalPolynomial(roots[2])), ") * (",
GF25.polyToString(GF25.minimalPolynomial(roots[3])), ") * (",
GF25.polyToString(GF25.minimalPolynomial(roots[4])), ")")
print()
# The roots create Φ_1,Φ_3,Φ_51
part1 = GF25.multPoly(GF25.minimalPolynomial(roots[2]),
GF25.minimalPolynomial(roots[3]))
part2 = GF25.multPoly(part1, GF25.minimalPolynomial(roots[4]))
print(GF25.polyToString(part2))
print("Exercise 4.5")
print("------------")
t = 2
C_BCH = BCHCode(GF25, t, True)
C_BCH.printInfo()
print("Exercise 4.6 (a)")
print("----------------")
poly1 = np.array([1, 1]) # (1 + X)
poly2 = np.array([1, 1, 0, 0, 1]) # (1 + X + X^4)
poly3 = np.array([1, 1, 1, 1, 1]) # (1 + X + X^2 + X^3 + X^4)
g = GF25.multPoly(GF25.multPoly(poly1, poly2), poly3)
n = 15
C_BCH = CyclicCode(g, n) # use CyclicCode because it allows to specify n
C_BCH.dmin(True)
print("Exercise 4.9")
print("------------")
pX = np.array([1, 1, 0, 0, 1]) # 1 + X + X^4
GF24 = GaloisField(pX)
#GF24.printInfo()
t = 2
C_BCH = BCHCode(GF24, t, True)
r = np.array([1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0])