r"""
Constructions of generator matrices using the GUAVA package for GAP

This module only contains Guava wrappers (GUAVA is an optional GAP package).

AUTHORS:

- David Joyner (2005-11-22, 2006-12-03): initial version

- Nick Alexander (2006-12-10): factor GUAVA code to guava.py

- David Joyner (2007-05): removed Golay codes, toric and trivial codes and
  placed them in code_constructions; renamed RandomLinearCode to
  RandomLinearCodeGuava

- David Joyner (2008-03): removed QR, XQR, cyclic and ReedSolomon codes

- David Joyner (2009-05): added "optional package" comments, fixed some
  docstrings to be sphinx compatible


REFERENCES:

.. [BM] Bazzi and Mitter, {\it Some constructions of codes from group actions}, (preprint
    March 2003, available on Mitter's MIT website).
"""
#*****************************************************************************
#       Copyright (C) 2007 David Joyner <wdj@usna.edu>
#                     2006 Nick Alexander <ncalexan@math.uci.edu>
#
#  Distributed under the terms of the GNU General Public License (GPL)
#
#                  http://www.gnu.org/licenses/
#*****************************************************************************
from __future__ import absolute_import

from sage.interfaces.all import gap
from sage.misc.randstate import current_randstate
from sage.matrix.matrix_space import MatrixSpace
from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
from sage.interfaces.gap import gfq_gap_to_sage
from .linear_code import LinearCode
from sage.features.gap import GapPackage


def QuasiQuadraticResidueCode(p):
    r"""
    A (binary) quasi-quadratic residue code (or QQR code).

    Follows the definition of Proposition 2.2 in [BM]. The code has a generator
    matrix in the block form `G=(Q,N)`. Here `Q` is a `p \times p` circulant
    matrix whose top row is `(0,x_1,...,x_{p-1})`, where `x_i=1` if and only if
    `i` is a quadratic residue `\mod p`, and `N` is a `p \times p` circulant
    matrix whose top row is `(0,y_1,...,y_{p-1})`, where `x_i+y_i=1` for all
    `i`.

    INPUT:

    - ``p`` -- a prime `>2`.

    OUTPUT:

    Returns a QQR code of length `2p`.

    EXAMPLES::

        sage: C = codes.QuasiQuadraticResidueCode(11); C   # optional - gap_packages (Guava package)
        [22, 11] linear code over GF(2)

    These are self-orthogonal in general and self-dual when $p \\equiv 3 \\pmod 4$.

    AUTHOR: David Joyner (11-2005)
    """
    GapPackage("guava", spkg="gap_packages").require()
    F = GF(2)
    gap.load_package("guava")
    gap.eval("C:=QQRCode(" + str(p) + ")")
    gap.eval("G:=GeneratorMat(C)")
    k = int(gap.eval("Length(G)"))
    n = int(gap.eval("Length(G[1])"))
    G = [[gfq_gap_to_sage(gap.eval("G[%s][%s]" % (i, j)), F)
          for j in range(1, n + 1)] for i in range(1, k + 1)]
    MS = MatrixSpace(F, k, n)
    return LinearCode(MS(G))


def RandomLinearCodeGuava(n, k, F):
    r"""
    The method used is to first construct a `k \times n` matrix of the block
    form `(I,A)`, where `I` is a `k \times k` identity matrix and `A` is a
    `k \times (n-k)` matrix constructed using random elements of `F`. Then
    the columns are permuted using a randomly selected element of the symmetric
    group `S_n`.

    INPUT:

    - ``n,k`` -- integers with `n>k>1`.

    OUTPUT:

    Returns a "random" linear code with length `n`, dimension `k` over field `F`.

    EXAMPLES::

        sage: C = codes.RandomLinearCodeGuava(30,15,GF(2)); C      # optional - gap_packages (Guava package)
        [30, 15] linear code over GF(2)
        sage: C = codes.RandomLinearCodeGuava(10,5,GF(4,'a')); C      # optional - gap_packages (Guava package)
        [10, 5] linear code over GF(4)

    AUTHOR: David Joyner (11-2005)
    """
    current_randstate().set_seed_gap()

    q = F.order()
    GapPackage("guava", spkg="gap_packages").require()
    gap.load_package("guava")
    gap.eval("C:=RandomLinearCode("+str(n)+","+str(k)+", GF("+str(q)+"))")
    gap.eval("G:=GeneratorMat(C)")
    k = int(gap.eval("Length(G)"))
    n = int(gap.eval("Length(G[1])"))
    G = [[gfq_gap_to_sage(gap.eval("G[%s][%s]" % (i, j)), F)
          for j in range(1, n + 1)] for i in range(1, k + 1)]
    MS = MatrixSpace(F, k, n)
    return LinearCode(MS(G))
