CoCalc -- weight

Path: Boolean-Cayley-graphs / boolean_cayley_graphs / weight_class.py
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r"""
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Classification of bent functions by their weight
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================================================
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The ``weight_class`` module defines the ``weight_class`` function,
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which returns the weight class corresponding to a weight.
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AUTHORS:
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- Paul Leopardi (2016-09-25): initial version
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EXAMPLES:
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::
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    sage: from boolean_cayley_graphs.weight_class import weight_class
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    sage: weight_class(4,1)
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    0
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    sage: weight_class(16,10)
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    1
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REFERENCES:
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Leopardi [Leo2017]_ Section 2.2.
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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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from sage.functions.other import sqrt
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def weight_class(length, weight):
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    r"""
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    Return the weight class corresponding to a given length and weight.
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    The length is the length of the truth table of a Boolean function.
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    The weight is the Hamming weight of the Boolean function.
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    INPUT:
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    - ``length`` -- positive integer:
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    - ``weight`` -- positive integer: the given Hamming weight.
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    OUTPUT:
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    An integer representing the weight class corresponding to ``length`` and
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    ``weight``.
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    EXAMPLES:
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    ::
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        sage: from boolean_cayley_graphs.weight_class import weight_class
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        sage: weight_class(4,1)
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        0
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        sage: weight_class(16,10)
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        1
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        sage: weight_class(16,6)
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        0
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        sage: weight_class(64,36)
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        1
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        sage: weight_class(63,37)
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        1
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        sage: weight_class(65,35)
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        0
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    .. NOTE::
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        The weight class really only makes sense for bent functions, for which
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        the weight class is either 0 or 1 [Leo2017]_.
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    REFERENCES:
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    Leopardi [Leo2017]_ Section 2.2.
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    """
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    sqrtlength = sqrt(length)
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    return int(((weight*2)/sqrtlength - sqrtlength + 1) / 2)
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