def time_information_set_steps():
before = time.clock()
while True:
I = sample(range(n), k)
Gi = G.matrix_from_columns(I)
try:
Gi_inv = Gi.inverse()
except ZeroDivisionError:
continue
return time.clock() - before
def time_information_set_steps():
before = time.clock()
while True:
I = sample(range(n), k)
Gi = G.matrix_from_columns(I)
try:
Gi_inv = Gi.inverse()
except ZeroDivisionError:
continue
return time.clock() - before
def decode(self, r):
r"""
The Lee-Brickell algorithm as described in the class doc.
Note that either parameters must be given at construction time or
:meth:`sage.coding.information_set_decoder.InformationSetAlgorithm.calibrate()`
should be called before calling this method.
INPUT:
- `r` -- a received word, i.e. a vector in the ambient space of
:meth:`decoder.Decoder.code`.
OUTPUT: A codeword whose distance to `r` satisfies ``self.decoding_interval()``.
EXAMPLES::
sage: M = matrix(GF(2), [[1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0],\
[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1],\
[0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0],\
[0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1],\
[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]])
sage: C = codes.LinearCode(M)
sage: from sage.coding.information_set_decoder import LeeBrickellISDAlgorithm
sage: A = LeeBrickellISDAlgorithm(C, (2,2))
sage: c = C.random_element()
sage: Chan = channels.StaticErrorRateChannel(C.ambient_space(), 2)
sage: r = Chan(c)
sage: c_out = A.decode(r)
sage: (r - c).hamming_weight() == 2
True
"""
import itertools
from sage.all import sample
C = self.code()
n, k = C.length(), C.dimension()
tau = self.decoding_interval()
p = self.parameters()['search_size']
F = C.base_ring()
G = C.generator_matrix()
Fstar = F.list()[1:]
while True:
# step 1.
I = sample(range(n), k)
Gi = G.matrix_from_columns(I)
try:
Gi_inv = Gi.inverse()
except ZeroDivisionError:
# I was not an information set
continue
Gt = Gi_inv * G
#step 2.
y = r - vector([r[i] for i in I]) * Gt
g = Gt.rows()
#step 3.
for pi in range(p + 1):
for A in itertools.combinations(range(k), pi):
for m in itertools.product(Fstar, repeat=pi):
e = y - sum(m[i] * g[A[i]] for i in range(pi))
errs = e.hamming_weight()
if errs >= tau[0] and errs <= tau[1]:
return r - e
def decode(self, r):
r"""
The Lee-Brickell algorithm as described in the class doc.
Note that either parameters must be given at construction time or
:meth:`sage.coding.information_set_decoder.InformationSetAlgorithm.calibrate()`
should be called before calling this method.
INPUT:
- `r` -- a received word, i.e. a vector in the ambient space of
:meth:`decoder.Decoder.code`.
OUTPUT: A codeword whose distance to `r` satisfies ``self.decoding_interval()``.
EXAMPLES::
sage: M = matrix(GF(2), [[1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0],\
[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1],\
[0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0],\
[0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1],\
[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]])
sage: C = codes.LinearCode(M)
sage: from sage.coding.information_set_decoder import LeeBrickellISDAlgorithm
sage: A = LeeBrickellISDAlgorithm(C, (2,2))
sage: c = C.random_element()
sage: Chan = channels.StaticErrorRateChannel(C.ambient_space(), 2)
sage: r = Chan(c)
sage: c_out = A.decode(r)
sage: (r - c).hamming_weight() == 2
True
"""
import itertools
from sage.all import sample
C = self.code()
n, k = C.length(), C.dimension()
tau = self.decoding_interval()
p = self.parameters()['search_size']
F = C.base_ring()
G = C.generator_matrix()
Fstar = F.list()[1:]
while True:
# step 1.
I = sample(range(n), k)
Gi = G.matrix_from_columns(I)
try:
Gi_inv = Gi.inverse()
except ZeroDivisionError:
# I was not an information set
continue
Gt = Gi_inv * G
#step 2.
y = r - vector([r[i] for i in I]) * Gt
g = Gt.rows()
#step 3.
for pi in range(p+1):
for A in itertools.combinations(range(k), pi):
for m in itertools.product(Fstar, repeat=pi):
e = y - sum(m[i]*g[A[i]] for i in range(pi))
errs = e.hamming_weight()
if errs >= tau[0] and errs <= tau[1]:
return r - e