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

src/sage/coding/abstract_code.py

@@ -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``
@@ -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
@@ -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
@@ -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)
 
@@ -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)
@@ -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)
         """

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]
 

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))

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]
         """