public static int[] CalculateSyndromes(GaloisFieldPolynomial poly, int numberOfSyndromes)
{
int[] syndromes = new int[numberOfSyndromes];
for (int i = 0; i < numberOfSyndromes; i++)
{
syndromes[i] = poly.EvaluateAt(_galoisField.Exp(i));
}
return syndromes;
}
public static int[] CorrectErrors(GaloisFieldPolynomial poly, int[] syndromes, int[] positions)
{
List<int> q = new List<int>();
q.Add(1);
int positionsCount = positions.Length;
int polyLength = poly.Coefficients.Length;
for (int i = 0; i < positionsCount; i++)
{
int x = _galoisField.Exp(polyLength - 1 - positions[i]);
q = GaloisFieldPolynomial.Multiply(q, new List<int>(new int[] { x, 1 }));
}
List<int> p = new List<int>();
for (int i = 0; i < positionsCount; i++)
{
p.Add(syndromes[i]);
}
p.Reverse();
p = GaloisFieldPolynomial.Multiply(p, q);
int pLength = p.Count;
List<int> pTemp = new List<int>();
for (int i = pLength - positionsCount; i < pLength; i++)
{
pTemp.Add(p[i]);
}
p = pTemp;
int qLength = q.Count;
int currentQPosition = 0;
if (qLength % 2 != 0) currentQPosition++;
List<int> qTemp = new List<int>();
for (; currentQPosition < qLength; currentQPosition += 2)
{
qTemp.Add(q[currentQPosition]);
}
q = qTemp;
int[] correctedOutput = new int[polyLength];
for (int i = 0; i < positionsCount; i++)
{
int x = _galoisField.Exp(positions[i] + 256 - polyLength);
int y = GaloisFieldPolynomial.Evaluate(p, x);
int z = GaloisFieldPolynomial.Evaluate(q, _galoisField.Multiply(x, x));
correctedOutput[positions[i]] ^= _galoisField.Divide(y, _galoisField.Multiply(x, z));
}
return correctedOutput;
}