static GF2pPolynomial CalculateSyndromes(GF2pPolynomial message, int eccLength)
{
int[] syndromes = new int[eccLength]; // add a zero at the front to simply later calculations
for (int i = 0; i < syndromes.Length; i++)
{
syndromes[i] = message.Evaluate(message.Field.Exp(i + 1)); // add 1 because we assume fcr == 1
}
return(new GF2pPolynomial(message.Field, syndromes, false));
}
static int[] Forney(GF2pPolynomial evaluator, int[] errorPositions, int startIndex)
{
int[] powers = new int[errorPositions.Length], magnitudes = new int[powers.Length - startIndex];
for (int i = 0; i < powers.Length; i++)
{
powers[i] = evaluator.Field.Exp(errorPositions[i]);
}
for (int i = 0; i < magnitudes.Length; i++)
{
int invPower = evaluator.Field.Invert(powers[i + startIndex]), divisor = 1;
for (int ei = 0; ei < powers.Length; ei++)
{
if (ei != i + startIndex)
{
divisor = evaluator.Field.Multiply(divisor, evaluator.Field.Multiply(powers[ei], invPower) ^ 1);
}
}
magnitudes[i] = evaluator.Field.Divide(evaluator.Evaluate(invPower), divisor);
}
return(magnitudes);
}
static int[] FindErrors(GF2pPolynomial locator, int dataLength)
{ // TODO: ideally we'd use the more efficient Chien's search here rather than this brute-force approach
int[] errorPositions = new int[locator.Degree];
int ei = 0;
for (int maxValue = (int)(locator.Field.Order - 1), di = 0; di < dataLength; di++)
{
if (locator.Evaluate(locator.Field.Exp(maxValue - di)) == 0)
{
if (ei != errorPositions.Length)
{
errorPositions[ei++] = di;
}
else
{
return(null);
}
}
}
return(ei == errorPositions.Length ? errorPositions : null);
}