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Issue #40513, #40514: Allow zero code and add intersection method #40564

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f54a30a
Trac #40513, #40514: Allow zero code and add intersection method
Hapsa21 Aug 9, 2025
8ad67ed
Merge branch 'develop' into fix-linear-code-intersection
Hapsa21 Aug 10, 2025
02d409e
Trac #40513, #40514: Allow zero code and add intersection method
Hapsa21 Aug 9, 2025
7e86f9e
Merge branch 'fix-linear-code-intersection' of https://github.com/Hap…
Hapsa21 Aug 10, 2025
0cb098b
Issue #40513, #40514: Allow zero code, add intersection, and fix CI
Hapsa21 Aug 13, 2025
933d848
Test: Add doctests for encode/decode with zero code
Hapsa21 Aug 13, 2025
a9ab529
Merge branch 'develop' into fix-linear-code-intersection
Hapsa21 Aug 16, 2025
6f6802c
Doc: Apply formatting suggestions from review
Hapsa21 Aug 16, 2025
1dbfa82
Doc: formatting
Hapsa21 Aug 16, 2025
d969d2f
Doc: Remove outdated comment about forbidding zero code
Hapsa21 Aug 18, 2025
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33 changes: 19 additions & 14 deletions src/sage/coding/abstract_code.py
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Original file line number Diff line number Diff line change
Expand Up @@ -215,7 +215,7 @@ def __init__(self, length, default_encoder_name=None,
INPUT:
- ``length`` -- the length of ``self`` (a Python int or a Sage Integer,
must be > 0)
must be >= 0)
- ``default_encoder_name`` -- (default: ``None``) the name of
the default encoder of ``self``
Expand Down Expand Up @@ -281,19 +281,24 @@ def __init__(self, length, default_encoder_name=None,
...
ValueError: length must be a Python int or a Sage Integer
If the length of the code is not a nonzero positive integer
(See :issue:`21326`), it will raise an exception::
If the length of the code is negative, it will raise an exception::
sage: C = MyCodeFamily(0)
sage: C = MyCodeFamily(-1)
Traceback (most recent call last):
...
ValueError: length must be a nonzero positive integer
ValueError: length must be a non-negative integer
Codes of length 0 are allowed::
sage: C = MyCodeFamily(0)
sage: C.length()
0
"""

if not isinstance(length, (int, Integer)):
raise ValueError("length must be a Python int or a Sage Integer")
if length <= 0:
raise ValueError("length must be a nonzero positive integer")
if length < 0:
raise ValueError("length must be a non-negative integer")

self._length = length
self._metric = metric
Expand Down Expand Up @@ -417,7 +422,7 @@ def __call__(self, m):
sage: C = LinearCode(G)
sage: word = vector((0, 1, 1, 0))
sage: C(word)
(1, 1, 0, 0, 1, 1, 0)
(0, 1, 1, 0, 0, 1, 1)
sage: c = C.random_element()
sage: C(c) == c
Expand Down Expand Up @@ -723,14 +728,14 @@ def decode_to_message(self, word, decoder_name=None, *args, **kwargs):
sage: C = LinearCode(G)
sage: word = vector(GF(2), (1, 1, 0, 0, 1, 1, 0))
sage: C.decode_to_message(word)
(0, 1, 1, 0)
(1, 1, 0, 0)
It is possible to manually choose the decoder amongst the list of the available ones::
sage: sorted(C.decoders_available())
['InformationSet', 'NearestNeighbor', 'Syndrome']
sage: C.decode_to_message(word, 'NearestNeighbor')
(0, 1, 1, 0)
(1, 1, 0, 0)
"""
return self.unencode(self.decode_to_code(word, decoder_name, *args, **kwargs), **kwargs)

Expand Down Expand Up @@ -882,17 +887,17 @@ def encode(self, word, encoder_name=None, *args, **kwargs):
sage: C = LinearCode(G)
sage: word = vector((0, 1, 1, 0))
sage: C.encode(word)
(1, 1, 0, 0, 1, 1, 0)
(0, 1, 1, 0, 0, 1, 1)
sage: C(word)
(1, 1, 0, 0, 1, 1, 0)
(0, 1, 1, 0, 0, 1, 1)
It is possible to manually choose the encoder amongst the list of the available ones::
sage: sorted(C.encoders_available())
['GeneratorMatrix', 'Systematic']
sage: word = vector((0, 1, 1, 0))
sage: C.encode(word, 'GeneratorMatrix')
(1, 1, 0, 0, 1, 1, 0)
(0, 1, 1, 0, 0, 1, 1)
"""
E = self.encoder(encoder_name, *args, **kwargs)
return E.encode(word)
Expand Down Expand Up @@ -1057,7 +1062,7 @@ def unencode(self, c, encoder_name=None, nocheck=False, **kwargs):
sage: G = Matrix(GF(2), [[1,1,1,0,0,0,0], [1,0,0,1,1,0,0],
....: [0,1,0,1,0,1,0], [1,1,0,1,0,0,1]])
sage: C = LinearCode(G)
sage: c = vector(GF(2), (1, 1, 0, 0, 1, 1, 0))
sage: c = vector(GF(2), (0, 1, 1, 0, 0, 1, 1))
sage: C.unencode(c)
(0, 1, 1, 0)
"""
Expand Down
134 changes: 99 additions & 35 deletions src/sage/coding/linear_code.py
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Original file line number Diff line number Diff line change
Expand Up @@ -80,17 +80,17 @@
sage: G = MS([[1,1,1,0,0,0,0], [1,0,0,1,1,0,0], [0,1,0,1,0,1,0], [1,1,0,1,0,0,1]])
sage: C = LinearCode(G)
sage: C.basis()
[(1, 1, 1, 0, 0, 0, 0),
(1, 0, 0, 1, 1, 0, 0),
(0, 1, 0, 1, 0, 1, 0),
(1, 1, 0, 1, 0, 0, 1)]
[(1, 0, 0, 0, 0, 1, 1),
(0, 1, 0, 0, 1, 0, 1),
(0, 0, 1, 0, 1, 1, 0),
(0, 0, 0, 1, 1, 1, 1)]
sage: c = C.basis()[1]
sage: c in C
True
sage: c.nonzero_positions()
[0, 3, 4]
[1, 4, 6]
sage: c.support()
[0, 3, 4]
[1, 4, 6]
sage: c.parent()
Vector space of dimension 7 over Finite Field of size 2

Expand Down Expand Up @@ -1441,7 +1441,7 @@
sage: G = Matrix(GF(2), [[1,1,1,0,0,0,0], [1,0,0,1,1,0,0], [0,1,0,1,0,1,0], [1,1,0,1,0,0,1]])
sage: C = LinearCode(G)
sage: C._minimum_weight_codeword() # needs sage.libs.gap
(0, 1, 0, 1, 0, 1, 0)
(0, 0, 1, 0, 1, 1, 0)

TESTS:

Expand Down Expand Up @@ -2314,35 +2314,48 @@

sage: G = matrix(GF(2), [[0,0,0]])
sage: C = LinearCode(G)
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change the Line 2313: Forbid the zero vector space.

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I think you need to delete: Forbid the zero vector space (see :issue:17452 and :issue:6486)::

Traceback (most recent call last):
...
ValueError: this linear code contains no nonzero vector
sage: C
[3, 0] linear code over GF(2)
sage: C.dimension()
0
sage: C_dual = C.dual_code()
sage: C_dual
[3, 3] linear code over GF(2)
sage: C_dual.dimension() == C_dual.length()
True
"""

base_ring = generator.base_ring()
from sage.matrix.constructor import matrix

if isinstance(generator, AbstractLinearCode):
generator = generator.generator_matrix()

if hasattr(generator, 'basis'):
if generator.dimension() == 0:
G = matrix(generator.base_ring(), 0, generator.ambient_space().dimension())
else:
G = matrix(generator.basis())
else:
G = generator

base_ring = G.base_ring()
if not base_ring.is_field():
raise ValueError("'generator' must be defined on a field (not a ring)")

try:
basis = None
if hasattr(generator, "nrows"): # generator matrix case
if generator.rank() < generator.nrows():
basis = generator.row_space().basis()
else:
basis = generator.basis() # vector space etc. case
if basis is not None:
from sage.matrix.constructor import matrix
generator = matrix(base_ring, basis)
if generator.nrows() == 0:
raise ValueError("this linear code contains no nonzero vector")
except AttributeError:
# Assume input is an AbstractLinearCode, extract its generator matrix
generator = generator.generator_matrix()
if G.is_zero() or G.nrows() == 0:
super().__init__(base_ring, G.ncols(), "GeneratorMatrix", "Syndrome")
self._dimension = 0
self._generator_matrix = matrix(base_ring, 0, self.length())
self._minimum_distance = d
return

super().__init__(base_ring, generator.ncols(),
G_echelon = G.echelon_form()
generator_matrix = G_echelon.matrix_from_rows([i for i, r in enumerate(G_echelon) if not r.is_zero()])

super().__init__(base_ring, generator_matrix.ncols(),
"GeneratorMatrix", "Syndrome")
self._generator_matrix = generator
self._dimension = generator.rank()
self._generator_matrix = generator_matrix
self._dimension = self._generator_matrix.rank()
self._minimum_distance = d

def __hash__(self):
Expand Down Expand Up @@ -2382,7 +2395,58 @@
"""
return "[%s, %s]\\textnormal{ Linear code over }%s"\
% (self.length(), self.dimension(), self.base_ring()._latex_())

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src/sage/coding/linear_code.py:2398:1: W293 Blank line contains whitespace
def intersection(self, other):
"""
Return the intersection of this linear code with another.
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The docstring should be a short summary on the first line, followed by a longer summary in subsequent paragraphs, like...

Return the intersection of this linear code with another.

The intersection of two linear codes C1 and C2 is the set of all...


The intersection of two linear codes C1 and C2 is the set of all
codewords that are in both C1 and C2. It is also a linear code.

This is computed using the identity:
C1 ∩ C2 = (C1_dual + C2_dual)_dual

INPUT:
- ``other`` -- a linear code.

OUTPUT:
- a linear code, the intersection of self and other.

EXAMPLES:
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This should be EXAMPLES:: with two colons and a blank line after it

sage: F = GF(2)
sage: G1 = matrix(F, [[1,1,0,0], [0,0,1,1]])
sage: C1 = LinearCode(G1)
sage: G2 = matrix(F, [[1,0,1,0], [0,1,0,1]])
sage: C2 = LinearCode(G2)
sage: C_int = C1.intersection(C2)
sage: C_int
[4, 1] linear code over GF(2)
sage: c = vector(F, (1,1,1,1))
sage: c in C_int
True

# Test intersection with the zero code
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Should be Test intersection with the zero code:: with a blank line after it. (The :: starts a code block in RST and without it, the doctest runner won't recognize this as a test.)

sage: C_zero = LinearCode(matrix(F, [[0,0,0,0]]))
sage: C1.intersection(C_zero)
[4, 0] linear code over GF(2)
"""
if not isinstance(other, AbstractLinearCode):
raise TypeError("Intersection is only defined between linear codes.")
if self.base_field() != other.base_field():
raise TypeError("Codes must be over the same base field.")
if self.length() != other.length():
raise ValueError("Codes must have the same length.")

C1_dual = self.dual_code()
C2_dual = other.dual_code()

G1d = C1_dual.generator_matrix()
G2d = C2_dual.generator_matrix()
G_sum = G1d.stack(G2d)
sum_of_duals = LinearCode(G_sum)

return sum_of_duals.dual_code()

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src/sage/coding/linear_code.py:2449:1: W293 Blank line contains whitespace
def generator_matrix(self, encoder_name=None, **kwargs):
r"""
Return a generator matrix of ``self``.
Expand All @@ -2401,8 +2465,8 @@
sage: G = matrix(GF(3),2,[1,-1,1,-1,1,1])
sage: code = LinearCode(G)
sage: code.generator_matrix()
[1 2 1]
[2 1 1]
[1 2 0]
[0 0 1]
"""
if encoder_name is None or encoder_name == 'GeneratorMatrix':
g = self._generator_matrix
Expand Down Expand Up @@ -2493,10 +2557,10 @@
sage: C = LinearCode(G)
sage: E = codes.encoders.LinearCodeGeneratorMatrixEncoder(C)
sage: E.generator_matrix()
[1 1 1 0 0 0 0]
[1 0 0 1 1 0 0]
[0 1 0 1 0 1 0]
[1 1 0 1 0 0 1]
[1 0 0 0 0 1 1]
[0 1 0 0 1 0 1]
[0 0 1 0 1 1 0]
[0 0 0 1 1 1 1]
"""
g = self.code().generator_matrix()
g.set_immutable()
Expand Down
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