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function gfcs = gfcosets(m, p)
// This function produces cyclotomic cosets for a Galois field GF(P)
//
// Calling Sequence
// GFCS = GFCOSETS(M)
// GFCS = GFCOSETS(M, P)
//
// Description
// GFCS = GFCOSETS(M) produces cyclotomic cosets mod(2^M - 1). Each row of the
// output GFCS contains one cyclotomic coset.
//
// GFCS = GFCOSETS(M, P) produces cyclotomic cosets mod(P^M - 1), where
// P is a prime number.
//
// Because the length of the cosets varies in the complete set, %nan is used to
// fill out the extra space in order to make all variables have the same
// length in the output matrix GFCS.
// Examples
// c = gfcosets(2,3)
// disp(c)
// See also
// gfminpol, gfprimdf, gfroots
// Authors
// Pola Lakshmi Priyanka, IIT Bombay//
//*************************************************************************************************************************************//
//Input argument check
[out_a,inp_a]=argn(0)
// Error Checking
if inp_a < 2
p = 2;
elseif ( isempty(p) | ~isscalar(p) | abs(p)~=p | floor(p)~=p | length(factor(p))~=1 | p==1)
error('comm:gfcosets: P should be a positive prime number');
end
if ( isempty(m) | ~isscalar(m) | ~isreal(m) | floor(m)~=m | m<1 )
error('comm:gfcosets: M should be a positive integer');
end
//Initialization
if ( ( p == 2 ) & ( m == 1 ) )
i = [];
else
i = 1;
end
n = p^m - 1;
gfcs = [];
mk = ones(1, n - 1);
while ~isempty(i)
mk(i) = 0;
s = i;
j = s;
pk = modulo(p*s, n);
//compute cyclotomic coset for s=i
while (pk > s)
mk(pk) = 0;
j = [j pk];
pk = modulo(pk * p, n);
end;
// append the coset to gfcs
[row_cs, col_cs] = size(gfcs);
[row_j, col_j ] = size(j);
if (col_cs == col_j) | (row_cs == 0)
gfcs = [gfcs; j];
elseif (col_cs > col_j)
gfcs = [gfcs; [j, ones(1, col_cs - col_j) * %nan]];
else
gfcs = [[gfcs, ones(row_cs, col_j - col_cs) * %nan]; j];
end;
i = find(mk == 1,1); // find the index of next number.
end;
// adding "0" to the first coset
[row_cs, col_cs] = size(gfcs);
gfcs = [[0, ones(1, col_cs - 1) * %nan]; gfcs];
endfunction
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