Merge of previous 'rank metric channel' enhancement #39117
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@@ -36,10 +36,18 @@ | |
| transmitted message | ||
| - :class:`ErrorErasureChannel`, which creates a specific number of errors and a | ||
| specific number of erasures in each transmitted message | ||
| - :class:`StaticRankErrorChannel`, which creates an error of specific rank in each | ||
| transmitted message. This is the rank analogue of :class:`StaticErrorRateChannel` | ||
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| AUTHORS: | ||
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| - David Lucas (2015): initial version | ||
| - Maxime Bombar (2021): Rank metric channel | ||
| """ | ||
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| # **************************************************************************** | ||
| # Copyright (C) 2015 David Lucas <[email protected]> | ||
| # Copyright (C) 2021 Maxime Bombar <[email protected]> | ||
| # | ||
| # This program is free software: you can redistribute it and/or modify | ||
| # it under the terms of the GNU General Public License as published by | ||
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@@ -49,15 +57,17 @@ | |
| # **************************************************************************** | ||
| from copy import copy | ||
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| from sage.categories.cartesian_product import cartesian_product | ||
| from sage.categories.fields import Fields | ||
| from sage.functions.other import binomial | ||
| from sage.matrix.constructor import matrix | ||
| from sage.misc.abstract_method import abstract_method | ||
| from sage.misc.prandom import randint, random, sample | ||
| from sage.modules.free_module import VectorSpace, span | ||
| from sage.modules.free_module_element import vector | ||
| from sage.rings.finite_rings.finite_field_constructor import GF | ||
| from sage.rings.integer import Integer | ||
| from sage.structure.sage_object import SageObject | ||
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| def random_error_vector(n, F, error_positions): | ||
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@@ -550,8 +560,8 @@ | |
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| def transmit_unsafe(self, message): | ||
| r""" | ||
| Return ``message`` with as many errors as ``self._number_errors`` | ||
| in it, and as many erasures as ``self._number_erasures`` in it. | ||
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| If ``self._number_errors`` was passed as a tuple for the number of errors, it will | ||
| pick a random integer between the bounds of the tuple and use it as the number of errors. | ||
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| """ | ||
| return sum(self.probability_of_exactly_t_errors(i) | ||
| for i in range(t+1)) | ||
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| class StaticRankErrorChannel(Channel): | ||
| r""" | ||
| Channel which adds an error of static rank to each message it transmits. | ||
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| The input space and the output space of this channel are the same. | ||
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| INPUT: | ||
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| - ``space`` -- the space of both input and output | ||
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| - ``rank_errors`` -- the rank of the error added to each transmitted message | ||
| It can be either an integer of a tuple. If a tuple is passed as | ||
| argument, the rank of the error will be a random integer between the | ||
| two bounds of the tuple. | ||
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| - ``relative_field`` -- The field to which the extension is relative. | ||
| If not given, it will default to the prime_subfield of the ambient space | ||
| base_field. | ||
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There was a problem hiding this comment.
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| EXAMPLES: | ||
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| We construct a StaticRankErrorChannel which adds error of rank 2 | ||
| to any transmitted message:: | ||
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There was a problem hiding this comment.
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| sage: n_err = 2 | ||
| sage: Chan = channels.StaticRankErrorChannel(GF(256)^6, n_err) | ||
| sage: Chan | ||
| Channel creating error of rank 2 over Finite Field of size 2, | ||
| of input and output space Vector space of dimension 6 | ||
| over Finite Field in z8 of size 2^8 | ||
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| We can also pass a tuple for the number of errors:: | ||
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| sage: n_err = (1, 4) | ||
| sage: Chan = channels.StaticRankErrorChannel(GF(256)^6, n_err) | ||
| sage: Chan | ||
| Channel creating error of rank between 1 and 4 over Finite Field | ||
| of size 2, of input and output space Vector space of dimension 6 | ||
| over Finite Field in z8 of size 2^8 | ||
| """ | ||
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| def __init__(self, space, rank_errors, relative_field=None): | ||
| r""" | ||
| TESTS: | ||
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| If the number of errors exceeds the dimension of the input space, | ||
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There was a problem hiding this comment. How about r"""
Initialize.
TESTS:? |
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| or the field extension degree, then an error is raised:: | ||
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| sage: n_err = 7 | ||
| sage: channels.StaticRankErrorChannel(GF(256)^6, n_err) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: There might be errors of rank larger than the dimension of the input space. | ||
| sage: channels.StaticRankErrorChannel(GF(64)^8, n_err) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: There might be errors of rank larger than the field extension degree. | ||
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| If ``relative_field`` is specified and is not a subfield of the base field, | ||
| it will return an error:: | ||
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| sage: n_err = 2 | ||
| sage: Chan = channels.StaticRankErrorChannel(GF(16)^6, n_err, GF(8)) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: Finite Field in z4 of size 2^4 is not an extension of | ||
| Finite Field in z3 of size 2^3 | ||
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| If ``relative_field`` is specified and is not a field, | ||
| it will return an error:: | ||
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| sage: n_err = 2 | ||
| sage: Chan = channels.StaticRankErrorChannel(GF(16)^6, n_err, GF(4)^2) | ||
| Traceback (most recent call last): | ||
| ... | ||
| ValueError: relative_field must be a Field and | ||
| Vector space of dimension 2 over Finite Field in z2 | ||
| of size 2^2 is not. | ||
| """ | ||
| if isinstance(rank_errors, (Integer, int)): | ||
| rank_errors = (rank_errors, rank_errors) | ||
| if not isinstance(rank_errors, (tuple, list)): | ||
| raise ValueError("rank_errors must be a tuple, a list, an Integer or a Python int") | ||
| super(StaticRankErrorChannel, self).__init__(space, space) | ||
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| if rank_errors[1] > space.dimension(): | ||
| raise ValueError("There might be errors of rank larger than the dimension of the input space.") | ||
| self._rank_errors = rank_errors | ||
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| self._base_field = space.base_field() | ||
| if not relative_field: | ||
| self._relative_field = self._base_field.prime_subfield() | ||
| else: | ||
| if relative_field not in Fields(): | ||
| raise ValueError("relative_field must be a Field and %s is not." % relative_field) | ||
| if not relative_field.is_subring(self._base_field): | ||
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There was a problem hiding this comment. ? ? |
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| raise ValueError("%s is not an extension of %s" % (self._base_field, relative_field)) | ||
| self._relative_field = relative_field | ||
| V, vec_to_field, field_to_vec = self._base_field.vector_space(self._relative_field) | ||
| self._column_space = V | ||
| self._extension_degree = V.dimension() | ||
| if rank_errors[1] > self._extension_degree: | ||
| raise ValueError("There might be errors of rank larger than the field extension degree.") | ||
| self._map_to_field = vec_to_field | ||
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| def _repr_(self): | ||
| r""" | ||
| Return a string representation of ``self``. | ||
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| EXAMPLES:: | ||
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| sage: n_err = 2 | ||
| sage: Chan = channels.StaticRankErrorChannel(GF(256)^6, n_err) | ||
| sage: Chan | ||
| Channel creating error of rank 2 over Finite Field of size 2, | ||
| of input and output space Vector space of dimension 6 | ||
| over Finite Field in z8 of size 2^8 | ||
| """ | ||
| no_err = self.rank_errors() | ||
| return "Channel creating error of rank %s over %s, of input and output space %s"\ | ||
| % (format_interval(no_err), self._relative_field, self.input_space()) | ||
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| def _latex_(self): | ||
| r""" | ||
| Return a latex representation of ``self``. | ||
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| EXAMPLES:: | ||
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| sage: n_err = 2 | ||
| sage: Chan = channels.StaticRankErrorChannel(GF(256)^6, n_err) | ||
| sage: latex(Chan) | ||
| \textnormal{Channel creating error of rank 2 over Finite Field | ||
| of size 2, of input and output space Vector space of dimension 6 | ||
| over Finite Field in z8 of size 2^8} | ||
| """ | ||
| no_err = self.rank_errors() | ||
| return "\\textnormal{Channel creating error of rank %s over %s, of input and output space %s}"\ | ||
| % (format_interval(no_err), self._relative_field, self.input_space()) | ||
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| def transmit_unsafe(self, message): | ||
| r""" | ||
| Return ``message`` with as many errors as ``self._rank_errors`` in it. | ||
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| If ``self._rank_errors`` was passed as a tuple for the number of errors, it will | ||
| pick a random integer between the bounds of the tuple and use it as the number of errors. | ||
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| This method does not check if ``message`` belongs to the input space of``self``. | ||
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| INPUT: | ||
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| - ``message`` -- a vector | ||
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| OUTPUT: | ||
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| - a vector of the output space | ||
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There was a problem hiding this comment. |
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| EXAMPLES:: | ||
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| sage: F = GF(16)^6 | ||
| sage: n_err = 2 | ||
| sage: Chan = channels.StaticRankErrorChannel(F, n_err, GF(4)) | ||
| sage: set_random_seed(10) | ||
| sage: msg = F.random_element() | ||
| sage: msg | ||
| (z4 + 1, z4, z4^3 + z4 + 1, z4^3 + z4^2 + z4 + 1, z4^2, z4^2) | ||
| sage: c = Chan.transmit_unsafe(msg) | ||
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| TESTS:: | ||
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| sage: from sage.coding.linear_rank_metric import rank_distance | ||
| sage: rank_distance(msg, c, GF(4)) | ||
| 2 | ||
| """ | ||
| rank_errors = randint(*self.rank_errors()) | ||
| Fq = self._relative_field | ||
| V = self._column_space | ||
| n = self.input_space().dimension() | ||
| good = False | ||
| while not good: | ||
| basis = [V.random_element() for i in range(rank_errors)] | ||
| R = span(basis) | ||
| err = [R.random_element() for i in range(n)] | ||
| M = matrix(Fq, err) | ||
| good = (M.rank() == rank_errors) | ||
| e = vector(map(self._map_to_field, M.rows())) | ||
| w = message + e | ||
| return w | ||
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| def rank_errors(self): | ||
| r""" | ||
| Return the number of rank errors created by ``self``. | ||
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| EXAMPLES:: | ||
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| sage: n_err = 3 | ||
| sage: Chan = channels.StaticRankErrorChannel(GF(256)^6, n_err) | ||
| sage: Chan.rank_errors() | ||
| (3, 3) | ||
| """ | ||
| return self._rank_errors | ||
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| def number_errors(self): | ||
| r""" | ||
| Return the number of errors created by ``self``. | ||
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| .. NOTE:: | ||
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| This function is here to ease the life of people coming from the Hamming world. | ||
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| EXAMPLES:: | ||
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| sage: n_err = 3 | ||
| sage: Chan = channels.StaticRankErrorChannel(GF(256)^6, n_err) | ||
| sage: Chan.number_errors() | ||
| (3, 3) | ||
| """ | ||
| return self._rank_errors | ||
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message. It can beIt can be either an integer or a tuple?