if delta > base**power - 1:
print 'Delta must be <=', base**power - 1
sys.exit(1)
# Generate $GF(q^n)$ for $q=base $n$=power and find our root of unity
GFqn = GFpoly(base, power)
alpha = nth_root_of_unity(GFqn, base**power - 1)
# Calculate the generator polynomial $G(x) = \prod_{i=1}^{\delta}{(x - \alpha^i)}$
Gpoly = Polynomial((GFqn(1),))
for b in range(1, delta):
Gpoly *= Polynomial((-(alpha ** b), GFqn(1)))
codeword_len = base**power - 1
message_len = base**power - len(Gpoly)
# Compute the codeword corresponding to the message [1, 2, ... message_len]
message = Polynomial([GFqn(i + 1) for i in range(message_len)])
codeword = message * Gpoly
print 'Alpha =', alpha.tonumber()
print 'g(x) =', Gpoly
print 'Message', message.asvector(), 'maps to', codeword.asvector()
print 'message % g(x) =', message % Gpoly
print 'codeword % g(x) =', codeword % Gpoly
maxErrors = (codeword_len - message_len) // 2
print 'Can detect', codeword_len - message_len, 'errors'
print 'Can correct', maxErrors, 'errors'
if delta > base**power - 1:
print 'Delta must be <=', base**power - 1
sys.exit(1)
# Generate $GF(q^n)$ for $q=base $n$=power and find our root of unity
GFqn = GFpoly(base, power)
alpha = nth_root_of_unity(GFqn, base**power - 1)
# Calculate the generator polynomial $G(x) = \prod_{i=1}^{\delta}{(x - \alpha^i)}$
Gpoly = Polynomial((GFqn(1), ))
for b in range(1, delta):
Gpoly *= Polynomial((-(alpha**b), GFqn(1)))
codeword_len = base**power - 1
message_len = base**power - len(Gpoly)
# Compute the codeword corresponding to the message [1, 2, ... message_len]
message = Polynomial([GFqn(i + 1) for i in range(message_len)])
codeword = message * Gpoly
print 'Alpha =', alpha.tonumber()
print 'g(x) =', Gpoly
print 'Message', message.asvector(), 'maps to', codeword.asvector()
print 'message % g(x) =', message % Gpoly
print 'codeword % g(x) =', codeword % Gpoly
maxErrors = (codeword_len - message_len) // 2
print 'Can detect', codeword_len - message_len, 'errors'
print 'Can correct', maxErrors, 'errors'
