CoCalc -- binary_projective_two_weight

Path: Boolean-Cayley-graphs / boolean_cayley_graphs / binary_projective_two_weight_codes.py
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r"""
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Some binary projective two-weight codes
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=======================================
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The ``binary_projective_two_weight_codes`` module defines
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functions that construct two types of binary projective two-weight codes
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as published by Tonchev [Ton1996]_ [Ton2007]_.
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AUTHORS:
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- Paul Leopardi (2016-09-15): initial version
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EXAMPLES:
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::
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    sage: from boolean_cayley_graphs.binary_projective_two_weight_codes import binary_projective_two_weight_27_6_12
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    sage: c27=binary_projective_two_weight_27_6_12()
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    sage: c27[1]
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    ('000000000000000111111111111',
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    '000000000111111000000111111',
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    '000111111000011000011000011',
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    '001000111011101000101000101',
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    '010001011101110011101011101',
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    '100010101000101001111101000')
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REFERENCES:
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Tonchev [Ton1996]_, [Ton2007]_.
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"""
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#*****************************************************************************
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#       Copyright (C) 2016-2017 Paul Leopardi [email protected]
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#
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#  Distributed under the terms of the GNU General Public License (GPL)
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#  as published by the Free Software Foundation; either version 2 of
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#  the License, or (at your option) any later version.
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#                  http://www.gnu.org/licenses/
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#*****************************************************************************
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def binary_projective_two_weight_27_6_12():
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    r"""
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    Return the binary projective two-weight [27,6,12] codes as published by Tonchev.
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    Return a tuple that encodes the generator matrices
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    of the binary projective two-weight [27,6,12] codes,
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    listed as codes 1, 2, 3a, 3b and 4 in Table 1 of Tonchev [Ton1996]_,
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    and repeated as codes 1 to 5 in Table 1.155 of Tonchev [Ton2007]_.
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    INPUT:
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    - None.
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    OUTPUT:
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    A tuple of tuples of strings. Each tuple of strings encodes a generator matrix
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    of a binary projective two-weight code.
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    EXAMPLES:
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    ::
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        sage: from boolean_cayley_graphs.binary_projective_two_weight_codes import binary_projective_two_weight_27_6_12
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        sage: c27=binary_projective_two_weight_27_6_12()
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        sage: c27[0]
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        ('000000000001111111111111111',
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        '000000011110000000011111111',
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        '000001100110000111100001111',
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        '000111111110011001100110011',
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        '011010101010111011101110100',
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        '101010101100001110111011101')
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    REFERENCES:
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    Tonchev [Ton1996]_ [Ton2007]_.
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    """
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    c1=("000000000001111111111111111",
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        "000000011110000000011111111",
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        "000001100110000111100001111",
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        "000111111110011001100110011",
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        "011010101010111011101110100",
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        "101010101100001110111011101")
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    c2=("000000000000000111111111111",
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        "000000000111111000000111111",
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        "000111111000011000011000011",
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        "001000111011101000101000101",
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        "010001011101110011101011101",
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        "100010101000101001111101000")
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    c3=("000000000000000111111111111",
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        "000000011111111000011111111",
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        "000001100001111001100001111",
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        "001110100010001010101110001",
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        "010110101110111110000110110",
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        "100011100110011111110010011")
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    c4=("000000000000000111111111111",
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        "000000011111111000000001111",
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        "000001100001111000011110011",
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        "001110100010111011101110101",
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        "010110101110001100100110000",
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        "111010010100011001101010000")
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    c5=("000000000000000111111111111",
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        "000000000111111000000111111",
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        "000000111000111000111000111",
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        "000111001001001011011000011",
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        "011001011010110001101001000",
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        "101010110011010000010010101")
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    return (c1, c2, c3, c4, c5)
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def binary_projective_two_weight_35_6_16():
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    r"""
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    Return the binary projective two-weight [35,6,16] codes as published by Tonchev.
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    Return a tuple that encodes the generator matrices
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    of the binary projective two-weight [35,6,16] codes, listed
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    as codes 1, 2a, 2b, 3a, 3b, 4a and 4b in Table 2 of Tonchev [Ton1996]_,
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    and repeated as codes 1 to 7 in Table 1.156 of Tonchev [Ton2007]_.
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    INPUT:
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    - None.
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    OUTPUT:
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    A tuple of tuples of strings. Each tuple of strings encodes a generator matrix
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    of a binary projective two-weight code.
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    EXAMPLES:
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    ::
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        sage: from boolean_cayley_graphs.binary_projective_two_weight_codes import binary_projective_two_weight_35_6_16
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        sage: c35=binary_projective_two_weight_35_6_16()
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        sage: c35[2]
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        ('00000000000000011111111111111111111',
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        '00000000011111100000000001111111111',
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        '00011111100001100001111110000111111',
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        '00100011101110101110001110111000111',
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        '01000101110111000010110010001011001',
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        '10001010100010110100010100011101011')
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    REFERENCES:
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    Tonchev [Ton1996]_ [Ton2007]_.
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    """
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    c1=("00000000000000000001111111111111111",
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        "00000000000111111110000000011111111",
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        "00000111111000000110000111100001111",
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        "00011000011000011110011001100110011",
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        "01101001101001101010111010001000100",
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        "10101010110010110100001000100011101")
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    c2=("00000000000000000001111111111111111",
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        "00000000011111111110000001111111111",
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        "00011111100001111110000110000111111",
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        "00100011100010001110001010111000111",
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        "01000101100100010110111010001011001",
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        "10001010101110110010011110011101011")
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    c3=("00000000000000011111111111111111111",
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        "00000000011111100000000001111111111",
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        "00011111100001100001111110000111111",
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        "00100011101110101110001110111000111",
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        "01000101110111000010110010001011001",
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        "10001010100010110100010100011101011")
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    c4=("00000000000000000001111111111111111",
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        "00000000000111111110000000011111111",
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        "00000111111000011110000001100001111",
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        "00111000111000101110001110100010001",
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        "01011011001011100010010010001100110",
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        "10001001010001110100100101100110011")
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    c5=("00000000000000000001111111111111111",
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        "00000000000111111110000000011111111",
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        "00000111111000011110000111100000011",
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        "00111000111011101110111000100011101",
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        "01011011001000100011001011001101100",
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        "11101101011001100110011101010110100")
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    c6=("00000000000000000001111111111111111",
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        "00000000000111111110000000011111111",
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        "00000011111000111110000011100000111",
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        "00011100111001001110001101101111011",
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        "01100101001010000110110110110011000",
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        "10101000011011011011011101010101101")
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    c7=("00000000000000000001111111111111111",
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        "00000000000111111110000000011111111",
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        "00000011111000111110001111100011111",
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        "00011100111001001110110001100000011",
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        "01100101001010000110010010100101111",
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        "10101000011011011010000110101000101")
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    return (c1, c2, c3, c4, c5, c6, c7)
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