Issue #40513, #40514: Allow zero code, add intersection, and fix CI

Hapsa21 · Hapsa21 · commit 0cb098bc7dcc · 2025-08-13T13:21:26.000+05:30
diff --git a/src/sage/coding/databases.py b/src/sage/coding/databases.py
@@ -232,10 +232,10 @@ def self_orthogonal_binary_codes(n, k, b=2, parent=None, BC=None, equal=False,
         [4, 1] linear code over GF(2)
         [1 1 1 1]
         [6, 2] linear code over GF(2)
-        [1 1 1 1 0 0]
+        [1 0 1 0 1 1]
         [0 1 0 1 1 1]
         [7, 3] linear code over GF(2)
-        [1 0 1 1 0 1 0]
+        [1 0 0 1 1 0 1]
         [0 1 0 1 1 1 0]
         [0 0 1 0 1 1 1]
 
@@ -248,7 +248,7 @@ def self_orthogonal_binary_codes(n, k, b=2, parent=None, BC=None, equal=False,
         [4, 1] linear code over GF(2)
         [1 1 1 1]
         [6, 2] linear code over GF(2)
-        [1 1 1 1 0 0]
+        [1 0 1 0 1 1]
         [0 1 0 1 1 1]
 
     Generate all self-orthogonal codes of length equal to 8 and
@@ -263,8 +263,8 @@ def self_orthogonal_binary_codes(n, k, b=2, parent=None, BC=None, equal=False,
         [0 0 1 0 0 1 0 0]
         [0 0 0 0 0 0 1 1]
         [8, 4] linear code over GF(2)
-        [1 0 0 1 1 0 1 0]
-        [0 1 0 1 1 1 0 0]
+        [1 0 0 0 1 1 0 1]
+        [0 1 0 0 1 0 1 1]
         [0 0 1 0 1 1 1 0]
         [0 0 0 1 0 1 1 1]
 
diff --git a/src/sage/coding/decoder.py b/src/sage/coding/decoder.py
@@ -293,7 +293,7 @@ def decode_to_message(self, r):
             sage: w_err = word + vector(GF(2), (1, 0, 0, 0, 0, 0, 0))
             sage: D = C.decoder()
             sage: D.decode_to_message(w_err)
-            (0, 1, 1, 0)
+            (1, 1, 0, 0)
         """
         self.defaulting_decode_to_message = True
         return self.code().unencode(self.decode_to_code(r))
diff --git a/src/sage/coding/encoder.py b/src/sage/coding/encoder.py
@@ -149,7 +149,7 @@ def encode(self, word):
             sage: word = vector(GF(2), (0, 1, 1, 0))
             sage: E = codes.encoders.LinearCodeGeneratorMatrixEncoder(C)
             sage: E.encode(word)
-            (1, 1, 0, 0, 1, 1, 0)
+            (0, 1, 1, 0, 0, 1, 1)
 
         If ``word`` is not in the message space of ``self``, it will return an exception::
 
@@ -183,7 +183,7 @@ def __call__(self, m):
             sage: word = vector(GF(2), (0, 1, 1, 0))
             sage: E = codes.encoders.LinearCodeGeneratorMatrixEncoder(C)
             sage: E(word)
-            (1, 1, 0, 0, 1, 1, 0)
+            (0, 1, 1, 0, 0, 1, 1)
 
             sage: F = GF(11)
             sage: Fx.<x> = F[]
@@ -224,7 +224,7 @@ def unencode(self, c, nocheck=False):
             True
             sage: E = codes.encoders.LinearCodeGeneratorMatrixEncoder(C)
             sage: E.unencode(c)
-            (0, 1, 1, 0)
+            (1, 1, 0, 0)
 
         TESTS:
 
@@ -241,11 +241,10 @@ def unencode(self, c, nocheck=False):
 
         Note that since :issue:`21326`, codes cannot be of length zero::
 
-            sage: G = Matrix(GF(17), [])
+            sage: G = matrix(GF(2), 0, 0)
             sage: C = LinearCode(G)
-            Traceback (most recent call last):
-            ...
-            ValueError: length must be a nonzero positive integer
+            sage: C
+            [0, 0] linear code over GF(2)
         """
         if not nocheck and c not in self.code():
             raise EncodingError("Given word is not in the code")
@@ -268,10 +267,10 @@ def _unencoder_matrix(self):
             sage: E = C.encoder()
             sage: E._unencoder_matrix()
             (
-            [0 0 1 1]
-            [0 1 0 1]
-            [1 1 1 0]
-            [0 1 1 1], (0, 1, 2, 3)
+            [1 0 0 0]
+            [0 1 0 0]
+            [0 0 1 0]
+            [0 0 0 1], (0, 1, 2, 3)
             )
         """
         info_set = self.code().information_set()
@@ -306,7 +305,7 @@ def unencode_nocheck(self, c):
             True
             sage: E = codes.encoders.LinearCodeGeneratorMatrixEncoder(C)
             sage: E.unencode_nocheck(c)
-            (0, 1, 1, 0)
+            (1, 1, 0, 0)
 
         Taking a vector that does not belong to ``C`` will not raise an error but
         probably just give a non-sensical result::
@@ -316,7 +315,7 @@ def unencode_nocheck(self, c):
             False
             sage: E = codes.encoders.LinearCodeGeneratorMatrixEncoder(C)
             sage: E.unencode_nocheck(c)
-            (0, 1, 1, 0)
+            (1, 1, 0, 0)
             sage: m = vector(GF(2), (0, 1, 1, 0))
             sage: c1 = E.encode(m)
             sage: c == c1
@@ -375,10 +374,10 @@ def generator_matrix(self):
             sage: C = LinearCode(G)
             sage: E = C.encoder()
             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]
         """
 
 
diff --git a/src/sage/coding/linear_code.py b/src/sage/coding/linear_code.py
@@ -2318,11 +2318,6 @@ def __init__(self, generator, d=None):
             [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
         """
 
         from sage.matrix.constructor import matrix
@@ -2399,7 +2394,6 @@ def _latex_(self):
     def intersection(self, other):
         """
         Return the intersection of this linear code with another.
-
         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.
 
@@ -2452,7 +2446,6 @@ def generator_matrix(self, encoder_name=None, **kwargs):
         Return a generator matrix of ``self``.
 
         INPUT:
-
         - ``encoder_name`` -- (default: ``None``) name of the encoder which will be
           used to compute the generator matrix. ``self._generator_matrix``
           will be returned if default value is kept.
@@ -3127,4 +3120,4 @@ def decoding_radius(self):
 LinearCode._registered_encoders["GeneratorMatrix"] = LinearCodeGeneratorMatrixEncoder
 
 LinearCodeSyndromeDecoder._decoder_type = {"hard-decision", "dynamic"}
-LinearCodeNearestNeighborDecoder._decoder_type = {"hard-decision", "always-succeed", "complete"}
+LinearCodeNearestNeighborDecoder._decoder_type = {"hard-decision", "always-succeed", "complete"}
diff --git a/src/sage/coding/linear_code_no_metric.py b/src/sage/coding/linear_code_no_metric.py
@@ -238,8 +238,8 @@ def generator_matrix(self, encoder_name=None, **kwargs):
             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]
         """
         E = self.encoder(encoder_name, **kwargs)
         return E.generator_matrix()
@@ -528,8 +528,8 @@ def systematic_generator_matrix(self, systematic_positions=None):
             ....:                    [ 2, 1, 1, 1]])
             sage: C = LinearCode(G)
             sage: C.generator_matrix()
-            [1 2 1 0]
-            [2 1 1 1]
+            [1 2 0 1]
+            [0 0 1 2]
             sage: C.systematic_generator_matrix()
             [1 2 0 1]
             [0 0 1 2]
@@ -762,7 +762,7 @@ def __getitem__(self, i):
             sage: G = Matrix(GF(3), [[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[24]
-            (2, 2, 0, 1, 2, 2, 0)
+            (0, 2, 2, 0, 0, 2, 1)
             sage: C[24] == C.list()[24]
             True
 
