// *************************************************
// * Public Class Methods *
// *************************************************
public static BinaryGaloisFieldElement[] createGeneratorPolynomial(BinaryGaloisField gf, Int32 maxCorrectibleErrorCnt)
{
// Generator polynomial, g(x), is of order 2s, so has 2s+1 coefficients
BinaryGaloisFieldElement[] g = new BinaryGaloisFieldElement[2 * maxCorrectibleErrorCnt + 1];
// Make g(x) = 1
g[0] = 1;
for (int i = 1; i <= (2 * maxCorrectibleErrorCnt); i++)
{
// Always make coefficient of x^i term equal to 1
g[i] = 1;
// Below multiply (g(x) = g[0] + g[1]*x + ... + g[i]*(x^i)) by (x - alpha^i)
for (int j = (i - 1); j > 0; j--)
{
if (g[j] != 0)
{
g[j] = g[j - 1] - gf.Multiply(gf.AlphaFromIndex(i), g[j]);
}
else
{
g[j] = g[j - 1];
}
}
// Coefficient of x^0 term is alpha^(1+2+...+i)
g[0] = gf.AlphaFromIndex(((i * (i + 1)) / 2));
}
return(g);
}
// *************************************************
// * Public Instance Methods *
// *************************************************
public Int32[] GenerateParity(Int32[] messageData)
{
Int32[] retArray = new Int32[2 * s];
BinaryGaloisFieldElement[] data = new BinaryGaloisFieldElement[N];
if (messageData.Length != k)
{
throw new ArgumentException("Wrong size.", "messageData");
}
// Parity is defined parityPoly(x) = x^2s * messagePoly(x) (mod generatorPoly(x))
// Convert input message data to array of BinaryGaloisFieldElement (implicit cast)
// Create x^2s * messagePoly(x) by shifting data up by 2s positions
for (int i = 0; i < k; i++)
{
data[i + (2 * s)] = messageData[i];
}
// Now do long division using generatorPoly, remainder is parity data
// Use synthetic division since generatorPoly is monic
for (int i = N - 1; i >= (2 * s); i--)
{
if (data[i] != 0)
{
for (int j = 1; j <= (2 * s); j++)
{
data[i - j] = data[i - j] - galoisField.Multiply(data[i], generatorPoly[2 * s - j]);
}
// Set to zero
data[i] = 0;
}
}
// Copy 2*s pieces of data to the parity symbols array
for (int i = 0; i < (2 * s); i++)
{
retArray[i] = (Int32)data[i];
}
// Return parity symbols
return(retArray);
}
// *************************************************
// * Public Class Methods *
// *************************************************
public static BinaryGaloisFieldElement[] createGeneratorPolynomial(BinaryGaloisField gf, Int32 maxCorrectibleErrorCnt)
{
// Generator polynomial, g(x), is of order 2s, so has 2s+1 coefficients
BinaryGaloisFieldElement[] g = new BinaryGaloisFieldElement[2*maxCorrectibleErrorCnt + 1];
// Make g(x) = 1
g[0] = 1;
for (int i = 1; i<=(2*maxCorrectibleErrorCnt); i++)
{
// Always make coefficient of x^i term equal to 1
g[i] = 1;
// Below multiply (g(x) = g[0] + g[1]*x + ... + g[i]*(x^i)) by (x - alpha^i)
for (int j=(i-1); j > 0; j--)
{
if (g[j] != 0)
g[j] = g[j - 1] - gf.Multiply(gf.AlphaFromIndex(i),g[j]);
else
g[j] = g[j - 1];
}
// Coefficient of x^0 term is alpha^(1+2+...+i)
g[0] = gf.AlphaFromIndex( ((i*(i+1))/2) );
}
return g;
}
