private int[] FindErrorLocations(GenericGfPoly errorLocator)
{
int numErrors = errorLocator.Degree;
if (numErrors == 1)
{
return(new[] { errorLocator.GetCoefficient(1) });
}
int[] result = new int[numErrors];
int e = 0;
for (int i = 1; i < field.Size && e < numErrors; i++)
{
if (errorLocator.EvaluateAt(i) == 0)
{
result[e] = field.Inverse(i);
e++;
}
}
if (e != numErrors)
{
return(null);
}
return(result);
}
private int[] FindErrorMagnitudes(GenericGfPoly errorEvaluator, int[] errorLocations)
{
int s = errorLocations.Length;
int[] result = new int[s];
for (int i = 0; i < s; i++)
{
int xiInverse = field.Inverse(errorLocations[i]);
int denominator = 1;
for (int j = 0; j < s; j++)
{
if (i != j)
{
int term = field.Multiply(errorLocations[j], xiInverse);
int termPlus1 = (term & 0x1) == 0 ? term | 1 : term & ~1;
denominator = field.Multiply(denominator, termPlus1);
}
}
result[i] = field.Multiply(errorEvaluator.EvaluateAt(xiInverse), field.Inverse(denominator));
if (field.GeneratorBase != 0)
{
result[i] = field.Multiply(result[i], xiInverse);
}
}
return(result);
}
internal GenericGfPoly[] RunEuclideanAlgorithm(GenericGfPoly a, GenericGfPoly b, int R)
{
if (a.Degree < b.Degree)
{
GenericGfPoly temp = a;
a = b;
b = temp;
}
GenericGfPoly rLast = a;
GenericGfPoly r = b;
GenericGfPoly tLast = field.Zero;
GenericGfPoly t = field.One;
while (r.Degree >= R / 2)
{
GenericGfPoly rLastLast = rLast;
GenericGfPoly tLastLast = tLast;
rLast = r;
tLast = t;
if (rLast.IsZero)
{
return(null);
}
r = rLastLast;
GenericGfPoly q = field.Zero;
int denominatorLeadingTerm = rLast.GetCoefficient(rLast.Degree);
int dltInverse = field.Inverse(denominatorLeadingTerm);
while (r.Degree >= rLast.Degree && !r.IsZero)
{
int degreeDiff = r.Degree - rLast.Degree;
int scale = field.Multiply(r.GetCoefficient(r.Degree), dltInverse);
q = q.AddOrSubtract(field.BuildMonomial(degreeDiff, scale));
r = r.AddOrSubtract(rLast.MultiplyByMonomial(degreeDiff, scale));
}
t = q.Multiply(tLast).AddOrSubtract(tLastLast);
if (r.Degree >= rLast.Degree)
{
return(null);
}
}
int sigmaTildeAtZero = t.GetCoefficient(0);
if (sigmaTildeAtZero == 0)
{
return(null);
}
int inverse = field.Inverse(sigmaTildeAtZero);
GenericGfPoly sigma = t.Multiply(inverse);
GenericGfPoly omega = r.Multiply(inverse);
return(new[] { sigma, omega });
}
public bool Decode(int[] received, int twoS)
{
var poly = new GenericGfPoly(field, received);
var syndromeCoefficients = new int[twoS];
var noError = true;
for (var i = 0; i < twoS; i++)
{
var eval = poly.EvaluateAt(field.Exp(i + field.GeneratorBase));
syndromeCoefficients[syndromeCoefficients.Length - 1 - i] = eval;
if (eval != 0)
{
noError = false;
}
}
if (noError)
{
return(true);
}
var syndrome = new GenericGfPoly(field, syndromeCoefficients);
var sigmaOmega = RunEuclideanAlgorithm(field.BuildMonomial(twoS, 1), syndrome, twoS);
if (sigmaOmega == null)
{
return(false);
}
var sigma = sigmaOmega[0];
var errorLocations = FindErrorLocations(sigma);
if (errorLocations == null)
{
return(false);
}
var omega = sigmaOmega[1];
var errorMagnitudes = FindErrorMagnitudes(omega, errorLocations);
for (var i = 0; i < errorLocations.Length; i++)
{
var position = received.Length - 1 - field.Log(errorLocations[i]);
if (position < 0)
{
return(false);
}
received[position] = GenericGf.AddOrSubtract(received[position], errorMagnitudes[i]);
}
return(true);
}