/** * Create a representation of GF(256) using the given primitive polynomial. * * @param primitive irreducible polynomial whose coefficients are represented by * the bits of an int, where the least-significant bit represents the constant * coefficient */ private GF256(int primitive) { expTable = new int[256]; logTable = new int[256]; int x = 1; for (int i = 0; i < 256; i++) { expTable[i] = x; x <<= 1; // x = x * 2; we're assuming the generator alpha is 2 if (x >= 0x100) { x ^= primitive; } } for (int i = 0; i < 255; i++) { logTable[expTable[i]] = i; } // logTable[0] == 0 but this should never be used zero = new GF256Poly(this, new int[]{0}); one = new GF256Poly(this, new int[]{1}); }
/** * Create a representation of GF(256) using the given primitive polynomial. * * @param primitive irreducible polynomial whose coefficients are represented by * the bits of an int, where the least-significant bit represents the constant * coefficient */ private GF256(int primitive) { expTable = new int[256]; logTable = new int[256]; int x = 1; for (int i = 0; i < 256; i++) { expTable[i] = x; x <<= 1; // x = x * 2; we're assuming the generator alpha is 2 if (x >= 0x100) { x ^= primitive; } } for (int i = 0; i < 255; i++) { logTable[expTable[i]] = i; } // logTable[0] == 0 but this should never be used zero = new GF256Poly(this, new int[]{0}); one = new GF256Poly(this, new int[]{1}); }
/** * @return the monomial representing coefficient * x^degree */ GF256Poly buildMonomial(int degree, int coefficient) { if (degree < 0) { throw new IllegalArgumentException(); } if (coefficient == 0) { return zero; } int[] coefficients = new int[degree + 1]; coefficients[0] = coefficient; return new GF256Poly(this, coefficients); }
/** * @return the monomial representing coefficient * x^degree */ GF256Poly buildMonomial(int degree, int coefficient) { if (degree < 0) { throw new IllegalArgumentException(); } if (coefficient == 0) { return zero; } int[] coefficients = new int[degree + 1]; coefficients[0] = coefficient; return new GF256Poly(this, coefficients); }
public ReedSolomonEncoder(GF256 field) { if (!GF256.QR_CODE_FIELD.equals(field)) { throw new IllegalArgumentException("Only QR Code is supported at this time"); } this.field = field; this.cachedGenerators = new Vector(); cachedGenerators.addElement(new GF256Poly(field, new int[] { 1 })); }
public ReedSolomonEncoder(GF256 field) { if (!GF256.QR_CODE_FIELD.equals(field)) { throw new IllegalArgumentException("Only QR Code is supported at this time"); } this.field = field; this.cachedGenerators = new Vector(); cachedGenerators.addElement(new GF256Poly(field, new int[] { 1 })); }
private GF256Poly buildGenerator(int degree) { if (degree >= cachedGenerators.size()) { GF256Poly lastGenerator = (GF256Poly) cachedGenerators.elementAt(cachedGenerators.size() - 1); for (int d = cachedGenerators.size(); d <= degree; d++) { GF256Poly nextGenerator = lastGenerator.multiply(new GF256Poly(field, new int[] { 1, field.exp(d - 1) })); cachedGenerators.addElement(nextGenerator); lastGenerator = nextGenerator; } } return (GF256Poly) cachedGenerators.elementAt(degree); }
private GF256Poly buildGenerator(int degree) { if (degree >= cachedGenerators.size()) { GF256Poly lastGenerator = (GF256Poly) cachedGenerators.elementAt(cachedGenerators.size() - 1); for (int d = cachedGenerators.size(); d <= degree; d++) { GF256Poly nextGenerator = lastGenerator.multiply(new GF256Poly(field, new int[] { 1, field.exp(d - 1) })); cachedGenerators.addElement(nextGenerator); lastGenerator = nextGenerator; } } return (GF256Poly) cachedGenerators.elementAt(degree); }
GF256Poly multiplyByMonomial(int degree, int coefficient) { if (degree < 0) { throw new IllegalArgumentException(); } if (coefficient == 0) { return field.getZero(); } int size = coefficients.length; int[] product = new int[size + degree]; for (int i = 0; i < size; i++) { product[i] = field.multiply(coefficients[i], coefficient); } return new GF256Poly(field, product); }
GF256Poly multiplyByMonomial(int degree, int coefficient) { if (degree < 0) { throw new IllegalArgumentException(); } if (coefficient == 0) { return field.getZero(); } int size = coefficients.length; int[] product = new int[size + degree]; for (int i = 0; i < size; i++) { product[i] = field.multiply(coefficients[i], coefficient); } return new GF256Poly(field, product); }
GF256Poly multiply(int scalar) { if (scalar == 0) { return field.getZero(); } if (scalar == 1) { return this; } int size = coefficients.length; int[] product = new int[size]; for (int i = 0; i < size; i++) { product[i] = field.multiply(coefficients[i], scalar); } return new GF256Poly(field, product); }
GF256Poly multiply(int scalar) { if (scalar == 0) { return field.getZero(); } if (scalar == 1) { return this; } int size = coefficients.length; int[] product = new int[size]; for (int i = 0; i < size; i++) { product[i] = field.multiply(coefficients[i], scalar); } return new GF256Poly(field, product); }
public void encode(int[] toEncode, int ecBytes) { if (ecBytes == 0) { throw new IllegalArgumentException("No error correction bytes"); } int dataBytes = toEncode.length - ecBytes; if (dataBytes <= 0) { throw new IllegalArgumentException("No data bytes provided"); } GF256Poly generator = buildGenerator(ecBytes); int[] infoCoefficients = new int[dataBytes]; System.arraycopy(toEncode, 0, infoCoefficients, 0, dataBytes); GF256Poly info = new GF256Poly(field, infoCoefficients); info = info.multiplyByMonomial(ecBytes, 1); GF256Poly remainder = info.divide(generator)[1]; int[] coefficients = remainder.getCoefficients(); int numZeroCoefficients = ecBytes - coefficients.length; for (int i = 0; i < numZeroCoefficients; i++) { toEncode[dataBytes + i] = 0; } System.arraycopy(coefficients, 0, toEncode, dataBytes + numZeroCoefficients, coefficients.length); }
public void encode(int[] toEncode, int ecBytes) { if (ecBytes == 0) { throw new IllegalArgumentException("No error correction bytes"); } int dataBytes = toEncode.length - ecBytes; if (dataBytes <= 0) { throw new IllegalArgumentException("No data bytes provided"); } GF256Poly generator = buildGenerator(ecBytes); int[] infoCoefficients = new int[dataBytes]; System.arraycopy(toEncode, 0, infoCoefficients, 0, dataBytes); GF256Poly info = new GF256Poly(field, infoCoefficients); info = info.multiplyByMonomial(ecBytes, 1); GF256Poly remainder = info.divide(generator)[1]; int[] coefficients = remainder.getCoefficients(); int numZeroCoefficients = ecBytes - coefficients.length; for (int i = 0; i < numZeroCoefficients; i++) { toEncode[dataBytes + i] = 0; } System.arraycopy(coefficients, 0, toEncode, dataBytes + numZeroCoefficients, coefficients.length); }
GF256Poly addOrSubtract(GF256Poly other) { if (!field.equals(other.field)) { throw new IllegalArgumentException("GF256Polys do not have same GF256 field"); } if (isZero()) { return other; } if (other.isZero()) { return this; } int[] smallerCoefficients = this.coefficients; int[] largerCoefficients = other.coefficients; if (smallerCoefficients.length > largerCoefficients.length) { int[] temp = smallerCoefficients; smallerCoefficients = largerCoefficients; largerCoefficients = temp; } int[] sumDiff = new int[largerCoefficients.length]; int lengthDiff = largerCoefficients.length - smallerCoefficients.length; // Copy high-order terms only found in higher-degree polynomial's coefficients System.arraycopy(largerCoefficients, 0, sumDiff, 0, lengthDiff); for (int i = lengthDiff; i < largerCoefficients.length; i++) { sumDiff[i] = GF256.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]); } return new GF256Poly(field, sumDiff); }
GF256Poly addOrSubtract(GF256Poly other) { if (!field.equals(other.field)) { throw new IllegalArgumentException("GF256Polys do not have same GF256 field"); } if (isZero()) { return other; } if (other.isZero()) { return this; } int[] smallerCoefficients = this.coefficients; int[] largerCoefficients = other.coefficients; if (smallerCoefficients.length > largerCoefficients.length) { int[] temp = smallerCoefficients; smallerCoefficients = largerCoefficients; largerCoefficients = temp; } int[] sumDiff = new int[largerCoefficients.length]; int lengthDiff = largerCoefficients.length - smallerCoefficients.length; // Copy high-order terms only found in higher-degree polynomial's coefficients System.arraycopy(largerCoefficients, 0, sumDiff, 0, lengthDiff); for (int i = lengthDiff; i < largerCoefficients.length; i++) { sumDiff[i] = GF256.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]); } return new GF256Poly(field, sumDiff); }
GF256Poly multiply(GF256Poly other) { if (!field.equals(other.field)) { throw new IllegalArgumentException("GF256Polys do not have same GF256 field"); } if (isZero() || other.isZero()) { return field.getZero(); } int[] aCoefficients = this.coefficients; int aLength = aCoefficients.length; int[] bCoefficients = other.coefficients; int bLength = bCoefficients.length; int[] product = new int[aLength + bLength - 1]; for (int i = 0; i < aLength; i++) { int aCoeff = aCoefficients[i]; for (int j = 0; j < bLength; j++) { product[i + j] = GF256.addOrSubtract(product[i + j], field.multiply(aCoeff, bCoefficients[j])); } } return new GF256Poly(field, product); }
GF256Poly multiply(GF256Poly other) { if (!field.equals(other.field)) { throw new IllegalArgumentException("GF256Polys do not have same GF256 field"); } if (isZero() || other.isZero()) { return field.getZero(); } int[] aCoefficients = this.coefficients; int aLength = aCoefficients.length; int[] bCoefficients = other.coefficients; int bLength = bCoefficients.length; int[] product = new int[aLength + bLength - 1]; for (int i = 0; i < aLength; i++) { int aCoeff = aCoefficients[i]; for (int j = 0; j < bLength; j++) { product[i + j] = GF256.addOrSubtract(product[i + j], field.multiply(aCoeff, bCoefficients[j])); } } return new GF256Poly(field, product); }
GF256Poly poly = new GF256Poly(field, received); int[] syndromeCoefficients = new int[twoS]; boolean dataMatrix = field.equals(GF256.DATA_MATRIX_FIELD); return; GF256Poly syndrome = new GF256Poly(field, syndromeCoefficients); GF256Poly[] sigmaOmega = runEuclideanAlgorithm(field.buildMonomial(twoS, 1), syndrome, twoS);