public BinaryGaloisFieldElement Divide(BinaryGaloisFieldElement x, BinaryGaloisFieldElement y)
{
Int32 result = 0x0;
Int32 ordX, ordY;
ordX = BinaryGaloisFieldElement.Order(x);
ordY = BinaryGaloisFieldElement.Order(y);
// if x is already of lower order than y, abort
if (ordX < ordY)
{
return((BinaryGaloisFieldElement)0);
}
// Perform long division
while (ordX >= ordY)
{
if ((x.Value & (0x1 << ordX)) != 0)
{
result = 0x1 << (ordX - ordY);
x -= (y << (ordX - ordY));
}
ordX--;
}
return((BinaryGaloisFieldElement)result);
}
// *************************************************
// * 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 BinaryGaloisFieldElement Modulo(BinaryGaloisFieldElement x, BinaryGaloisFieldElement y)
{
Int32 ordX, ordY;
ordX = BinaryGaloisFieldElement.Order(x);
ordY = BinaryGaloisFieldElement.Order(y);
// if x is already of lower order than y, abort
if (BinaryGaloisFieldElement.Order(x) < BinaryGaloisFieldElement.Order(y))
{
return(x);
}
// Keep subtracting mod value until we are in a valid range
// Perform long division
while (ordX >= ordY)
{
if ((x.Value & (0x1 << ordX)) != 0)
{
x -= (y << (ordX - ordY));
}
ordX--;
}
return(x);
}
// Array for access to alpha exponents
public Int32 IndexFromAlpha(BinaryGaloisFieldElement alpha)
{
if ((alpha.Value == 0) || (alpha.Value >= Length))
{
throw new ArgumentException("IndexFromAlpha: Out of range", "alpha");
}
return(this.index[alpha.Value]);
}
public override Boolean Equals(object obj)
{
if (!(obj is BinaryGaloisFieldElement))
{
return(false);
}
BinaryGaloisFieldElement x = (BinaryGaloisFieldElement)obj;
return((value == x.value));
}
// *************************************************
// * Public constructors *
// *************************************************
// *************************************************
// * Public methods *
// *************************************************
public static Int32 Order(BinaryGaloisFieldElement x)
{
UInt32 Mask = 0x80000000;
Int32 order = 31;
while (((x.Value & Mask) == 0x0) && (order > 0))
{
Mask >>= 1;
order--;
}
return(order);
}
// *************************************************
// * Public constructors *
// *************************************************
// Public constructor for Binary Galois Field class
// r is the exponent to which 2 is raised
public BinaryGaloisField(Int32 r)
{
// Set the irreducible polynomial for GF(2^r)
poly = (BinaryGaloisFieldElement)primPoly[r];
// Set the primitive element alpha
primElement = (BinaryGaloisFieldElement)2;
// Set the field length
length = (1 << r);
// Generate the field elements
GenerateFieldElements();
// Generate the alpha exponents
GenerateAlphaExponents();
}
// Assume field Elements are polynomials of max order 15
public BinaryGaloisFieldElement Multiply(BinaryGaloisFieldElement x, BinaryGaloisFieldElement y)
{
BinaryGaloisFieldElement tempVal = (BinaryGaloisFieldElement)0;
UInt32 mask = 0x1;
// Perform multiplication
for (int i = 0; i < 16; i++)
{
if ((x.Value & mask) != 0)
{
tempVal += (y << i);
}
mask <<= 1;
}
// Now take modulo poly
return(Modulo(tempVal, poly));
}
// *************************************************
// * 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 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 constructors *
// *************************************************
// Public constructor for Binary Galois Field class
// r is the exponent to which 2 is raised
public BinaryGaloisField(Int32 r)
{
// Set the irreducible polynomial for GF(2^r)
poly = (BinaryGaloisFieldElement) primPoly[r];
// Set the primitive element alpha
primElement = (BinaryGaloisFieldElement) 2;
// Set the field length
length = (1 << r);
// Generate the field elements
GenerateFieldElements();
// Generate the alpha exponents
GenerateAlphaExponents();
}
// *************************************************
// * Public constructors *
// *************************************************
// *************************************************
// * Public methods *
// *************************************************
public static Int32 Order(BinaryGaloisFieldElement x)
{
UInt32 Mask = 0x80000000;
Int32 order = 31;
while (((x.Value & Mask) == 0x0) && (order > 0))
{
Mask >>= 1;
order--;
}
return order;
}
// Array for access to alpha exponents
public Int32 IndexFromAlpha(BinaryGaloisFieldElement alpha)
{
if ( (alpha.Value == 0) || (alpha.Value >= Length) )
throw new ArgumentException("IndexFromAlpha: Out of range", "alpha");
return this.index[alpha.Value];
}
// Assume field Elements are polynomials of max order 15
public BinaryGaloisFieldElement Multiply(BinaryGaloisFieldElement x, BinaryGaloisFieldElement y)
{
BinaryGaloisFieldElement tempVal = (BinaryGaloisFieldElement) 0;
UInt32 mask = 0x1;
// Perform multiplication
for (int i = 0; i<16; i++)
{
if ((x.Value & mask) != 0)
{
tempVal += (y << i);
}
mask <<= 1;
}
// Now take modulo poly
return Modulo(tempVal,poly);
}
public BinaryGaloisFieldElement Divide(BinaryGaloisFieldElement x, BinaryGaloisFieldElement y)
{
Int32 result = 0x0;
Int32 ordX, ordY;
ordX = BinaryGaloisFieldElement.Order(x);
ordY = BinaryGaloisFieldElement.Order(y);
// if x is already of lower order than y, abort
if ( ordX < ordY)
return ((BinaryGaloisFieldElement) 0);
// Perform long division
while (ordX >= ordY)
{
if ( (x.Value & (0x1 << ordX)) != 0)
{
result = 0x1 << (ordX - ordY);
x -= (y << (ordX - ordY));
}
ordX--;
}
return ((BinaryGaloisFieldElement)result);
}
public BinaryGaloisFieldElement Modulo(BinaryGaloisFieldElement x, BinaryGaloisFieldElement y)
{
Int32 ordX, ordY;
ordX = BinaryGaloisFieldElement.Order(x);
ordY = BinaryGaloisFieldElement.Order(y);
// if x is already of lower order than y, abort
if (BinaryGaloisFieldElement.Order(x) < BinaryGaloisFieldElement.Order(y))
return x;
// Keep subtracting mod value until we are in a valid range
// Perform long division
while (ordX >= ordY)
{
if ( (x.Value & (0x1 << ordX)) != 0)
{
x -= (y << (ordX - ordY));
}
ordX--;
}
return x;
}
// *************************************************
// * 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;
}