This is the implementation of Generalized Reed-Solomon (GRS) Codes by Java.
Please contact junmingke1994@gmail.com if you have any question.
// decoding
// The first line contains one prime number which defines the field.
// The second line contains two parameters of the GRS code.
// The third line contains numbers separated by the spaces. Each number is a non-zero element represented as an integer in the given range.
// The fourth line contains numbers separated by the spaces. Each number is a non-zero element represented as an integer in the given range.
// The fifth line contains numbers separated by the spaces. Each number is an element represented as an integer in the given range.
int p = 7;
int n = 6, k = 2;
int d = n - k + 1;
int[] alpha = new int[]{1,2,3,4,5,6};
int[] v = new int[]{1,1,1,1,1,1};
int[] y = new int[]{1,2,5,4,5,1};
// expect output {1,2,3,4,5,6}
int[][] H = generateGRS(alpha, v, n, k, p);
int[] Sx = multiplyHY(H, y, p);
int[][] RTx = euclidPoly(Arrays.copyOfRange(Sx, 0, n - k), d, p);
int[][] errorLocator = polyRoot(RTx[1], p);
int[] derivativeTx = derivate(RTx[1], p);
int[] errorEvaluator = errorEvaluate(errorLocator, derivativeTx, RTx[0], p);
int[] codeword = polyMinus(p, y.length - 1, y, errorEvaluator.length - 1, errorEvaluator);