/// <summary>
/// Construct the check matrix of a Goppa code in canonical form from the irreducible Goppa polynomial over the finite field <c>GF(2^m)</c>.
/// </summary>
///
/// <param name="Field">The finite field</param>
/// <param name="Gp">The irreducible Goppa polynomial</param>
///
/// <returns>The new GF2Matrix</returns>
public static GF2Matrix CreateCanonicalCheckMatrix(GF2mField Field, PolynomialGF2mSmallM Gp)
{
int m = Field.Degree;
int n = 1 << m;
int t = Gp.Degree;
// create matrix H over GF(2^m)
int[][] hArray = ArrayUtils.CreateJagged <int[][]>(t, n);
// create matrix YZ
int[][] yz = ArrayUtils.CreateJagged <int[][]>(t, n);
if (ParallelUtils.IsParallel)
{
Parallel.For(0, n, j =>
yz[0][j] = Field.Inverse(Gp.EvaluateAt(j)));
}
else
{
// here j is used as index and as element of field GF(2^m)
for (int j = 0; j < n; j++)
{
yz[0][j] = Field.Inverse(Gp.EvaluateAt(j));
}
}
for (int i = 1; i < t; i++)
{
// here j is used as index and as element of field GF(2^m)
if (ParallelUtils.IsParallel)
{
Parallel.For(0, n, j =>
{
yz[i][j] = Field.Multiply(yz[i - 1][j], j);
});
}
else
{
for (int j = 0; j < n; j++)
{
yz[i][j] = Field.Multiply(yz[i - 1][j], j);
}
}
}
// create matrix H = XYZ
for (int i = 0; i < t; i++)
{
if (ParallelUtils.IsParallel)
{
Parallel.For(0, n, j =>
{
for (int k = 0; k <= i; k++)
{
hArray[i][j] = Field.Add(hArray[i][j], Field.Multiply(yz[k][j], Gp.GetCoefficient(t + k - i)));
}
});
}
else
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k <= i; k++)
{
hArray[i][j] = Field.Add(hArray[i][j], Field.Multiply(yz[k][j], Gp.GetCoefficient(t + k - i)));
}
}
}
}
// convert to matrix over GF(2)
int[][] result = ArrayUtils.CreateJagged <int[][]>(t * m, IntUtils.URShift((n + 31), 5));
if (ParallelUtils.IsParallel)
{
for (int j = 0; j < n; j++)
{
int q = IntUtils.URShift(j, 5);
int r = 1 << (j & 0x1f);
for (int i = 0; i < t; i++)
{
int e = hArray[i][j];
Parallel.For(0, m, u =>
{
int b = (IntUtils.URShift(e, u)) & 1;
if (b != 0)
{
int ind = (i + 1) * m - u - 1;
result[ind][q] ^= r;
}
});
}
}
}
else
{
for (int j = 0; j < n; j++)
{
int q = IntUtils.URShift(j, 5);
int r = 1 << (j & 0x1f);
for (int i = 0; i < t; i++)
{
int e = hArray[i][j];
for (int u = 0; u < m; u++)
{
int b = (IntUtils.URShift(e, u)) & 1;
if (b != 0)
{
int ind = (i + 1) * m - u - 1;
result[ind][q] ^= r;
}
}
}
}
}
return(new GF2Matrix(n, result));
}
/// <summary>
/// Construct the check matrix of a Goppa code in canonical form from the irreducible Goppa polynomial over the finite field <c>GF(2^m)</c>.
/// </summary>
///
/// <param name="Field">The finite field</param>
/// <param name="Gp">The irreducible Goppa polynomial</param>
///
/// <returns>The new GF2Matrix</returns>
public static GF2Matrix CreateCanonicalCheckMatrix(GF2mField Field, PolynomialGF2mSmallM Gp)
{
int m = Field.Degree;
int n = 1 << m;
int t = Gp.Degree;
// create matrix H over GF(2^m)
int[][] hArray = ArrayUtils.CreateJagged<int[][]>(t, n);
// create matrix YZ
int[][] yz = ArrayUtils.CreateJagged<int[][]>(t, n);
if (ParallelUtils.IsParallel)
{
Parallel.For(0, n, j =>
yz[0][j] = Field.Inverse(Gp.EvaluateAt(j)));
}
else
{
// here j is used as index and as element of field GF(2^m)
for (int j = 0; j < n; j++)
yz[0][j] = Field.Inverse(Gp.EvaluateAt(j));
}
for (int i = 1; i < t; i++)
{
// here j is used as index and as element of field GF(2^m)
if (ParallelUtils.IsParallel)
{
Parallel.For(0, n, j =>
{
yz[i][j] = Field.Multiply(yz[i - 1][j], j);
});
}
else
{
for (int j = 0; j < n; j++)
yz[i][j] = Field.Multiply(yz[i - 1][j], j);
}
}
// create matrix H = XYZ
for (int i = 0; i < t; i++)
{
if (ParallelUtils.IsParallel)
{
Parallel.For(0, n, j =>
{
for (int k = 0; k <= i; k++)
hArray[i][j] = Field.Add(hArray[i][j], Field.Multiply(yz[k][j], Gp.GetCoefficient(t + k - i)));
});
}
else
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k <= i; k++)
hArray[i][j] = Field.Add(hArray[i][j], Field.Multiply(yz[k][j], Gp.GetCoefficient(t + k - i)));
}
}
}
// convert to matrix over GF(2)
int[][] result = ArrayUtils.CreateJagged<int[][]>(t * m, IntUtils.URShift((n + 31), 5));
if (ParallelUtils.IsParallel)
{
for (int j = 0; j < n; j++)
{
int q = IntUtils.URShift(j, 5);
int r = 1 << (j & 0x1f);
for (int i = 0; i < t; i++)
{
int e = hArray[i][j];
Parallel.For(0, m, u =>
{
int b = (IntUtils.URShift(e, u)) & 1;
if (b != 0)
{
int ind = (i + 1) * m - u - 1;
result[ind][q] ^= r;
}
});
}
}
}
else
{
for (int j = 0; j < n; j++)
{
int q = IntUtils.URShift(j, 5);
int r = 1 << (j & 0x1f);
for (int i = 0; i < t; i++)
{
int e = hArray[i][j];
for (int u = 0; u < m; u++)
{
int b = (IntUtils.URShift(e, u)) & 1;
if (b != 0)
{
int ind = (i + 1) * m - u - 1;
result[ind][q] ^= r;
}
}
}
}
}
return new GF2Matrix(n, result);
}
