@@ -2981,8 +2981,6 @@ def random_element(self, *args, **kwds):
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c .set_immutable ()
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return c
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- < << << << HEAD
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- == == == =
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def rate (self ):
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r"""
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Return the ratio of the number of information symbols to
@@ -2996,7 +2994,6 @@ def rate(self):
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"""
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return self .dimension () / self .length ()
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- >> >> >> > 0 fa589622f71eb2a82f15a5e7eae7f8df6639cd1
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def redundancy_matrix (self ):
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r"""
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Returns the non-identity columns of a systematic generator matrix for
@@ -3374,37 +3371,21 @@ def standard_form(self, return_permutation=True):
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r"""
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Returns a linear code which is permutation-equivalent to ``self`` and
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admits a generator matrix in standard form.
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- <<<<<<< HEAD
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A generator matrix is in standard form if it is of the form `[I \vert
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A]`, where `I` is the `k \times k` identity matrix. Any code admits a
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generator matrix in systematic form, i.e. where a subset of the columns
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form the identity matrix, but one might need to permute columns to allow
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the identity matrix to be leading.
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- =======
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-
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- A generator matrix is in standard form if it is of the form `[I \vert
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- A]`, where `I` is the `k \times k` identity matrix. Any code admits a
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- generator matrix in systematic form, i.e. where a subset of the columns
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- form the identity matrix, but one might need to permute columns to allow
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- the identity matrix to be leading.
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-
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- >>>>>>> 0fa589622f71eb2a82f15a5e7eae7f8df6639cd1
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INPUT:
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- ``return_permutation`` -- (default: ``True``) if ``True``, the column
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permutation which brings ``self`` into the returned code is also
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returned.
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- <<<<<<< HEAD
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OUTPUT:
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- =======
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- OUTPUT:
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-
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- >>>>>>> 0fa589622f71eb2a82f15a5e7eae7f8df6639cd1
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- A :class:`LinearCode` whose :meth:`systematic_generator_matrix` is
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guaranteed to be of the form `[I \vert A]`.
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@@ -4185,19 +4166,11 @@ class LinearCodeSystematicEncoder(Encoder):
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``systematic_positions[0]``, the 1st index at position
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``systematic_positions[1]``, etc. A ``ValueError`` is raised at
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construction time if the supplied indices do not form an information set.
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- <<<<<<< HEAD
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-
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- EXAMPLES:
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- The following demonstrates the basic usage of :class:`LinearCodeSystematicEncoder`::
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-
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- =======
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EXAMPLES:
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The following demonstrates the basic usage of :class:`LinearCodeSystematicEncoder`::
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- >>>>>>> 0fa589622f71eb2a82f15a5e7eae7f8df6639cd1
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sage: G = Matrix(GF(2), [[1,1,1,0,0,0,0,0],\
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[1,0,0,1,1,0,0,0],\
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[0,1,0,1,0,1,0,0],\
@@ -4384,11 +4357,7 @@ def generator_matrix(self):
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[1 1 0 0 0 1 0]
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[0 0 1 0 0 1 0]
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[0 0 0 0 1 1 0]
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- <<<<<<< HEAD
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- [0 0 0 0 0 0 1]
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- =======
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[0 0 0 0 0 0 1]
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- >>>>>>> 0fa589622f71eb2a82f15a5e7eae7f8df6639cd1
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"""
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C = self .code ()
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# This if statement detects if this encoder is itself the default encoder.
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