/usr/share/octave/packages/communications-1.2.0/@galois/dftmtx.m is in octave-communications-common 1.2.0-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 | ## Copyright (C) 2002 David Bateman
##
## 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 the Free Software
## Foundation; either version 3 of the License, or (at your option) any later
## version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{d} =} dftmtx (@var{a})
##
## Form a matrix, that can be used to perform Fourier transforms in
## a Galois Field.
##
## Given that @var{a} is an element of the Galois Field GF(2^m), and
## that the minimum value for @var{k} for which @code{@var{a} ^ @var{k}}
## is equal to one is @code{2^m - 1}, then this function produces a
## @var{k}-by-@var{k} matrix representing the discrete Fourier transform
## over a Galois Field with respect to @var{a}. The Fourier transform of
## a column vector is then given by @code{dftmtx (@var{a}) * @var{x}}.
##
## The inverse Fourier transform is given by @code{dftmtx (1 / @var{a})}
## @end deftypefn
function d = dftmtx (a)
if (nargin != 1)
print_usage ();
endif
if (!isgalois (a))
error ("dftmtx: argument must be a galois variable");
endif
m = a.m;
prim = a.prim_poly;
n = 2^a.m - 1;
if (n > 255)
error (["dftmtx: argument must be in Galois Field GF(2^M)" ...
", where M is in the range [1,8]"]);
endif
if (length (a) != 1)
error ("dftmtx: argument must be a scalar");
endif
mp = minpol (a);
if (mp(1) != 1 || !isprimitive (mp))
error ("dftmtx: argument must be a primitive nth root of unity");
endif
step = log (a);
step = step.x;
row = exp (gf ([0:n-1], m, prim));
d = zeros (n);
for i = 1:n;
d(i,:) = row .^ mod (step*(i-1), n);
endfor
endfunction
%%Test input validation
%!error dftmtx (gf (1, 12))
%!error dftmtx (gf (eye (3), 4))
|