def test_diff_c(self):
"""
NOTE: Octave produces the incorrect result for shortened RS codes (https://savannah.gnu.org/bugs/?func=detailitem&item_id=60800)
Z = zeros(10, 4);
C = rsenc(gf([Z,M], 4), 15, 9, 3, 1);
C(:,5:end)
"""
c = 3
rs = galois.ReedSolomon(self.n, self.k, c=c)
GF = rs.field
M = GF(self.M)
C_truth = GF([
[ 0, 6, 15, 10, 5, 14, 3, 9, 12, 4, 7],
[ 0, 10, 0, 4, 15, 5, 4, 15, 13, 7, 6],
[ 2, 12, 3, 3, 8, 3, 11, 12, 8, 14, 14],
[13, 11, 0, 15, 3, 5, 6, 11, 5, 2, 4],
[ 2, 12, 9, 6, 8, 11, 12, 11, 6, 9, 6],
[10, 3, 8, 1, 7, 13, 14, 9, 15, 0, 3],
[ 0, 3, 3, 8, 0, 11, 10, 4, 2, 2, 4],
[ 5, 15, 5, 12, 13, 11, 9, 9, 7, 15, 5],
[14, 1, 3, 4, 15, 9, 9, 10, 14, 6, 6],
[14, 11, 15, 12, 8, 11, 3, 4, 9, 9, 7],
])
C = rs.encode(M)
assert type(C) is GF
assert np.array_equal(C, C_truth)
C = rs.encode(M, parity_only=True)
assert type(C) is GF
assert np.array_equal(C, C_truth[:, -(self.n - self.k):])
C = rs.encode(M.view(np.ndarray))
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth)
C = rs.encode(M.view(np.ndarray), parity_only=True)
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth[:, -(self.n - self.k):])
def test_diff_primitive_poly(self):
"""
NOTE: Octave produces the incorrect result for shortened RS codes (https://savannah.gnu.org/bugs/?func=detailitem&item_id=60800)
Z = zeros(10, 4);
C = rsenc(gf([Z,M], 4, 25), 15, 9, 'end');
C(:,5:end)
"""
p = galois.Poly.Degrees([4, 3, 0]) # galois.primitive_poly(2, 4, method="max")
rs = galois.ReedSolomon(self.n, self.k, primitive_poly=p)
GF = rs.field
M = GF(self.M)
C_truth = GF([
[ 0, 6, 15, 10, 5, 9, 15, 2, 10, 14, 14],
[ 0, 10, 0, 4, 15, 0, 4, 14, 0, 5, 7],
[ 2, 12, 3, 3, 8, 4, 3, 1, 7, 5, 6],
[13, 11, 0, 15, 3, 2, 1, 10, 1, 12, 8],
[ 2, 12, 9, 6, 8, 8, 3, 2, 9, 8, 13],
[10, 3, 8, 1, 7, 10, 9, 12, 15, 11, 2],
[ 0, 3, 3, 8, 0, 11, 8, 5, 9, 14, 10],
[ 5, 15, 5, 12, 13, 7, 9, 5, 2, 5, 11],
[14, 1, 3, 4, 15, 11, 9, 12, 2, 11, 7],
[14, 11, 15, 12, 8, 1, 1, 10, 8, 9, 6],
])
C = rs.encode(M)
assert type(C) is GF
assert np.array_equal(C, C_truth)
C = rs.encode(M, parity_only=True)
assert type(C) is GF
assert np.array_equal(C, C_truth[:, -(self.n - self.k):])
C = rs.encode(M.view(np.ndarray))
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth)
C = rs.encode(M.view(np.ndarray), parity_only=True)
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth[:, -(self.n - self.k):])
def test_default(self):
"""
NOTE: Octave produces the incorrect result for shortened RS codes (https://savannah.gnu.org/bugs/?func=detailitem&item_id=60800)
Z = zeros(10, 10);
C = rsenc(gf([Z,M], 5), 31, 23, 'end');
C(:,11:end)
"""
rs = galois.ReedSolomon(self.n, self.k)
GF = rs.field
M = GF(self.M)
C_truth = GF([
[ 0, 0, 7, 14, 23, 2, 9, 20, 10, 3, 25, 16, 30, 10, 8, 24, 30, 6, 9, 18, 8],
[17, 17, 11, 18, 16, 9, 13, 10, 24, 24, 26, 12, 8, 16, 6, 16, 19, 4, 17, 5, 13],
[29, 0, 0, 4, 22, 30, 20, 5, 23, 3, 16, 1, 4, 2, 8, 19, 27, 10, 28, 9, 22],
[ 4, 24, 21, 28, 25, 9, 27, 9, 23, 0, 22, 20, 24, 0, 31, 22, 31, 10, 24, 14, 30],
[26, 21, 4, 17, 15, 24, 28, 2, 28, 4, 19, 20, 26, 4, 20, 11, 28, 30, 10, 30, 15],
[13, 20, 5, 6, 6, 16, 31, 30, 15, 7, 10, 29, 3, 14, 7, 27, 0, 10, 6, 23, 28],
[31, 3, 18, 3, 15, 17, 19, 25, 27, 6, 12, 27, 28, 18, 27, 10, 31, 18, 4, 5, 15],
[14, 17, 11, 15, 3, 3, 1, 11, 4, 7, 10, 18, 4, 1, 31, 21, 25, 17, 15, 11, 21],
[ 9, 21, 17, 2, 3, 6, 24, 16, 19, 25, 10, 0, 30, 7, 19, 30, 27, 11, 8, 4, 7],
[17, 6, 17, 21, 15, 10, 31, 8, 27, 27, 21, 9, 15, 12, 24, 30, 8, 7, 12, 11, 19],
])
C = rs.encode(M)
assert type(C) is GF
assert np.array_equal(C, C_truth)
C = rs.encode(M, parity_only=True)
assert type(C) is GF
assert np.array_equal(C, C_truth[:, -(self.n - self.k):])
C = rs.encode(M.view(np.ndarray))
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth)
C = rs.encode(M.view(np.ndarray), parity_only=True)
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth[:, -(self.n - self.k):])
def test_diff_c(self):
"""
rsenc(gf(M, 5), 31, 23, 3, 1)
"""
c = 3
rs = galois.ReedSolomon(self.n, self.k, c=c)
GF = rs.field
M = GF(self.M)
C_truth = GF([
[26, 29, 13, 30, 28, 8, 8, 13, 12, 31, 15, 0, 18, 4, 13, 26, 7, 31, 28, 21, 31, 27, 12, 16, 24, 14, 26, 10, 1, 22, 26],
[14, 30, 13, 1, 31, 1, 11, 5, 19, 27, 3, 7, 30, 22, 16, 27, 22, 14, 28, 25, 12, 27, 0, 28, 6, 20, 24, 27, 7, 21, 13],
[16, 4, 7, 16, 24, 2, 18, 4, 27, 16, 8, 9, 20, 7, 2, 18, 2, 0, 6, 29, 19, 0, 9, 17, 18, 11, 8, 6, 1, 19, 19],
[19, 25, 16, 0, 24, 30, 24, 29, 18, 21, 9, 30, 14, 14, 26, 19, 13, 6, 29, 15, 3, 22, 5, 7, 3, 29, 18, 13, 25, 16, 2],
[ 2, 6, 4, 30, 6, 15, 21, 3, 13, 5, 15, 13, 15, 11, 27, 28, 30, 11, 24, 2, 22, 0, 2, 18, 31, 1, 2, 2, 16, 22, 19],
[23, 27, 5, 15, 12, 0, 2, 1, 9, 11, 8, 6, 1, 19, 8, 26, 26, 29, 5, 27, 4, 30, 28, 18, 15, 15, 4, 15, 28, 3, 8],
[11, 10, 21, 22, 22, 25, 26, 26, 10, 8, 4, 9, 30, 12, 13, 29, 9, 11, 11, 11, 21, 21, 17, 11, 11, 24, 2, 1, 14, 28, 26],
[ 1, 23, 28, 6, 27, 17, 4, 20, 31, 4, 0, 3, 8, 7, 9, 26, 9, 1, 30, 22, 15, 3, 14, 12, 8, 17, 12, 29, 22, 16, 20],
[12, 29, 20, 21, 2, 25, 9, 0, 12, 25, 2, 4, 11, 18, 26, 1, 20, 30, 9, 1, 28, 22, 3, 3, 3, 9, 17, 29, 14, 6, 9],
[31, 24, 26, 21, 15, 30, 19, 14, 17, 7, 13, 20, 13, 7, 14, 1, 17, 20, 28, 13, 13, 30, 19, 27, 3, 23, 17, 5, 8, 4, 23],
])
C = rs.encode(M)
assert type(C) is GF
assert np.array_equal(C, C_truth)
C = rs.encode(M, parity_only=True)
assert type(C) is GF
assert np.array_equal(C, C_truth[:, self.k:])
C = rs.encode(M.view(np.ndarray))
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth)
C = rs.encode(M.view(np.ndarray), parity_only=True)
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth[:, self.k:])
def test_diff_primitive_poly(self):
"""
rsenc(gf(M, 5, 61), 31, 23, 'end')
"""
p = galois.Poly.Degrees([5, 4, 3, 2, 0]) # galois.primitive_poly(2, 5, method="max")
rs = galois.ReedSolomon(self.n, self.k, primitive_poly=p)
GF = rs.field
M = GF(self.M)
C_truth = GF([
[26, 29, 13, 30, 28, 8, 8, 13, 12, 31, 15, 0, 18, 4, 13, 26, 7, 31, 28, 21, 31, 27, 12, 8, 25, 22, 27, 30, 16, 12, 1],
[14, 30, 13, 1, 31, 1, 11, 5, 19, 27, 3, 7, 30, 22, 16, 27, 22, 14, 28, 25, 12, 27, 0, 7, 14, 25, 30, 23, 5, 11, 15],
[16, 4, 7, 16, 24, 2, 18, 4, 27, 16, 8, 9, 20, 7, 2, 18, 2, 0, 6, 29, 19, 0, 9, 6, 19, 25, 1, 18, 21, 26, 25],
[19, 25, 16, 0, 24, 30, 24, 29, 18, 21, 9, 30, 14, 14, 26, 19, 13, 6, 29, 15, 3, 22, 5, 24, 30, 5, 17, 24, 20, 3, 15],
[ 2, 6, 4, 30, 6, 15, 21, 3, 13, 5, 15, 13, 15, 11, 27, 28, 30, 11, 24, 2, 22, 0, 2, 2, 15, 2, 10, 25, 30, 18, 13],
[23, 27, 5, 15, 12, 0, 2, 1, 9, 11, 8, 6, 1, 19, 8, 26, 26, 29, 5, 27, 4, 30, 28, 26, 9, 23, 3, 16, 4, 8, 31],
[11, 10, 21, 22, 22, 25, 26, 26, 10, 8, 4, 9, 30, 12, 13, 29, 9, 11, 11, 11, 21, 21, 17, 18, 5, 7, 30, 18, 6, 10, 8],
[ 1, 23, 28, 6, 27, 17, 4, 20, 31, 4, 0, 3, 8, 7, 9, 26, 9, 1, 30, 22, 15, 3, 14, 0, 7, 29, 27, 3, 19, 18, 3],
[12, 29, 20, 21, 2, 25, 9, 0, 12, 25, 2, 4, 11, 18, 26, 1, 20, 30, 9, 1, 28, 22, 3, 20, 2, 30, 29, 18, 7, 14, 7],
[31, 24, 26, 21, 15, 30, 19, 14, 17, 7, 13, 20, 13, 7, 14, 1, 17, 20, 28, 13, 13, 30, 19, 26, 31, 27, 7, 17, 26, 21, 16],
])
C = rs.encode(M)
assert type(C) is GF
assert np.array_equal(C, C_truth)
C = rs.encode(M, parity_only=True)
assert type(C) is GF
assert np.array_equal(C, C_truth[:, self.k:])
C = rs.encode(M.view(np.ndarray))
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth)
C = rs.encode(M.view(np.ndarray), parity_only=True)
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth[:, self.k:])
def test_diff_c(self):
"""
rsenc(gf(M, 4), 15, 9, 3, 1)
"""
c = 3
rs = galois.ReedSolomon(self.n, self.k, c=c)
GF = rs.field
M = GF(self.M)
C_truth = GF([
[ 5, 4, 13, 15, 6, 14, 8, 8, 10, 13, 0, 13, 7, 9, 3],
[14, 10, 14, 0, 13, 2, 11, 13, 15, 11, 3, 3, 15, 3, 14],
[ 8, 12, 7, 11, 4, 7, 12, 15, 7, 2, 9, 3, 13, 13, 14],
[10, 15, 1, 14, 3, 8, 13, 14, 12, 2, 6, 12, 15, 0, 13],
[12, 2, 15, 8, 3, 15, 6, 11, 4, 12, 13, 2, 12, 13, 1],
[ 5, 10, 0, 14, 0, 14, 3, 14, 7, 7, 4, 1, 13, 9, 5],
[ 0, 1, 1, 13, 14, 11, 12, 11, 3, 0, 6, 9, 3, 13, 10],
[ 4, 0, 0, 13, 8, 10, 12, 10, 13, 14, 0, 11, 8, 6, 14],
[ 2, 8, 10, 13, 8, 11, 5, 10, 5, 6, 0, 12, 10, 9, 3],
[ 9, 3, 4, 7, 3, 7, 6, 11, 15, 7, 14, 11, 8, 0, 12],
])
C = rs.encode(M)
assert type(C) is GF
assert np.array_equal(C, C_truth)
C = rs.encode(M, parity_only=True)
assert type(C) is GF
assert np.array_equal(C, C_truth[:, self.k:])
C = rs.encode(M.view(np.ndarray))
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth)
C = rs.encode(M.view(np.ndarray), parity_only=True)
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth[:, self.k:])
def test_diff_primitive_poly(self):
"""
rsenc(gf(M, 4, 25), 15, 9, 'end')
"""
p = galois.Poly.Degrees([4, 3, 0]) # galois.primitive_poly(2, 4, method="max")
rs = galois.ReedSolomon(self.n, self.k, primitive_poly=p)
GF = rs.field
M = GF(self.M)
C_truth = GF([
[ 5, 4, 13, 15, 6, 14, 8, 8, 10, 0, 6, 4, 1, 3, 7],
[14, 10, 14, 0, 13, 2, 11, 13, 15, 2, 3, 2, 1, 0, 10],
[ 8, 12, 7, 11, 4, 7, 12, 15, 7, 15, 8, 6, 8, 14, 12],
[10, 15, 1, 14, 3, 8, 13, 14, 12, 14, 9, 14, 15, 7, 4],
[12, 2, 15, 8, 3, 15, 6, 11, 4, 2, 1, 6, 0, 5, 4],
[ 5, 10, 0, 14, 0, 14, 3, 14, 7, 14, 11, 8, 2, 15, 2],
[ 0, 1, 1, 13, 14, 11, 12, 11, 3, 2, 3, 0, 7, 2, 6],
[ 4, 0, 0, 13, 8, 10, 12, 10, 13, 8, 1, 9, 8, 11, 9],
[ 2, 8, 10, 13, 8, 11, 5, 10, 5, 3, 15, 7, 13, 5, 0],
[ 9, 3, 4, 7, 3, 7, 6, 11, 15, 4, 1, 7, 1, 1, 14],
])
C = rs.encode(M)
assert type(C) is GF
assert np.array_equal(C, C_truth)
C = rs.encode(M, parity_only=True)
assert type(C) is GF
assert np.array_equal(C, C_truth[:, self.k:])
C = rs.encode(M.view(np.ndarray))
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth)
C = rs.encode(M.view(np.ndarray), parity_only=True)
assert type(C) is np.ndarray
assert np.array_equal(C, C_truth[:, self.k:])
def test_rs_generator_poly():
# S. Lin and D. Costello. Error Control Coding. Example 7.1, p. 238.
p = galois.primitive_poly(2, 6)
GF = galois.GF(2**6, irreducible_poly=p)
a = GF.primitive_element
assert galois.ReedSolomon(63, 57).generator_poly == galois.Poly(a**np.array([0, 59, 48, 43, 55, 10, 21]), field=GF)
# Octave rsgenpoly()
assert np.array_equal(galois.ReedSolomon(15, 13).generator_poly.coeffs, [1, 6, 8])
assert np.array_equal(galois.ReedSolomon(15, 11).generator_poly.coeffs, [1, 13, 12, 8, 7])
assert np.array_equal(galois.ReedSolomon(15, 9).generator_poly.coeffs, [1, 7, 9, 3, 12, 10, 12])
assert np.array_equal(galois.ReedSolomon(15, 7).generator_poly.coeffs, [1, 9, 4, 3, 4, 13, 6, 14, 12])
assert np.array_equal(galois.ReedSolomon(15, 5).generator_poly.coeffs, [1, 4, 8, 10, 12, 9, 4, 2, 12, 2, 7])
assert np.array_equal(galois.ReedSolomon(15, 3).generator_poly.coeffs, [1, 5, 9, 5, 8, 1, 4, 13, 9, 4, 12, 13, 8])
assert np.array_equal(galois.ReedSolomon(15, 1).generator_poly.coeffs, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
# Ensure we're using the correct default primitive polynomial
assert np.array_equal(galois.ReedSolomon(7, 5).generator_poly.coeffs, [1, 6, 3])
assert np.array_equal(galois.ReedSolomon(15, 9).generator_poly.coeffs, [1, 7, 9, 3, 12, 10, 12])
assert np.array_equal(galois.ReedSolomon(31, 25).generator_poly.coeffs, [1, 17, 26, 30, 27, 30, 24])
assert np.array_equal(galois.ReedSolomon(63, 57).generator_poly.coeffs, [1, 61, 13, 55, 46, 48, 59])
assert np.array_equal(galois.ReedSolomon(127, 121).generator_poly.coeffs, [1, 126, 64, 68, 100, 34, 109])
assert np.array_equal(galois.ReedSolomon(255, 249).generator_poly.coeffs, [1, 126, 4, 158, 58, 49, 117])
assert np.array_equal(galois.ReedSolomon(511, 505).generator_poly.coeffs, [1, 126, 254, 108, 222, 26, 76])
def test_repr():
rs = galois.ReedSolomon(15, 11)
assert repr(rs) == "<Reed-Solomon Code: [15, 11, 5] over GF(2^4)>"
class TestReedSolomon(Base):
code_sys = galois.ReedSolomon(63, 55)
code_non_sys = galois.ReedSolomon(63, 55, systematic=False)
GF = code_sys.field
N = 1_000