decode method

int decode(List<int> received, int numECCodewords, List<int>? erasures)

@param received received codewords @param numECCodewords number of those codewords used for EC @param erasures location of erasures @return number of errors @throws ChecksumException if errors cannot be corrected, maybe because of too many errors

Implementation

int decode(List<int> received, int numECCodewords, List<int>? erasures) {
  final poly = ModulusPoly(_field, received);
  final S = List.filled(numECCodewords, 0);
  bool error = false;
  for (int i = numECCodewords; i > 0; i--) {
    final eval = poly.evaluateAt(_field.exp(i));
    S[numECCodewords - i] = eval;
    if (eval != 0) {
      error = true;
    }
  }

  if (!error) {
    return 0;
  }

  ModulusPoly knownErrors = _field.one;
  if (erasures != null) {
    for (int erasure in erasures) {
      final b = _field.exp(received.length - 1 - erasure);
      // Add (1 - bx) term:
      final term = ModulusPoly(_field, [_field.subtract(0, b), 1]);
      knownErrors = knownErrors.multiplyPoly(term);
    }
  }

  final syndrome = ModulusPoly(_field, S);
  //syndrome = syndrome.multiply(knownErrors);

  final sigmaOmega = _runEuclideanAlgorithm(
    _field.buildMonomial(numECCodewords, 1),
    syndrome,
    numECCodewords,
  );
  final sigma = sigmaOmega[0];
  final omega = sigmaOmega[1];

  //sigma = sigma.multiply(knownErrors);

  final errorLocations = _findErrorLocations(sigma);
  final errorMagnitudes = _findErrorMagnitudes(omega, sigma, errorLocations);

  for (int i = 0; i < errorLocations.length; i++) {
    final position = received.length - 1 - _field.log(errorLocations[i]);
    if (position < 0) {
      throw ChecksumException.getChecksumInstance();
    }
    received[position] =
        _field.subtract(received[position], errorMagnitudes[i]);
  }
  return errorLocations.length;
}