Ejemplo n.º 1
0
        private GenericGFPoly BuildGenerator(int degree)
        {
            if (degree >= cachedGenerators.Count)
            {
                GenericGFPoly lastGenerator = cachedGenerators[cachedGenerators.Count - 1];

                for (int d = cachedGenerators.Count; d <= degree; d++)
                {
                    var nextGenerator = lastGenerator.Multiply(new GenericGFPoly(field, new int[] { 1, field.Exp(d - 1 + field.GeneratorBase) }));
                    cachedGenerators.Add(nextGenerator);
                    lastGenerator = nextGenerator;
                }
            }

            return(cachedGenerators[degree]);
        }
Ejemplo n.º 2
0
        internal GenericGFPoly[] RunEuclideanAlgorithm(GenericGFPoly a, GenericGFPoly b, int R)
        {
            // Assume a's degree is >= b's
            if (a.Degree < b.Degree)
            {
                GenericGFPoly temp = a;
                a = b;
                b = temp;
            }

            GenericGFPoly rLast = a;
            GenericGFPoly r     = b;
            GenericGFPoly tLast = field.Zero;
            GenericGFPoly t     = field.One;

            int halfR = R / 2;

            // Run Euclidean algorithm until r's degree is less than R/2
            while (r.Degree >= halfR)
            {
                GenericGFPoly rLastLast = rLast;
                GenericGFPoly tLastLast = tLast;

                rLast = r;
                tLast = t;

                // Divide rLastLast by rLast, with quotient in q and remainder in r
                if (rLast.IsZero)
                {
                    // Oops, Euclidean algorithm already terminated?
                    // throw new ReedSolomonException("r_{i-1} was zero");
                    return(null);
                }

                r = rLastLast;

                GenericGFPoly q = field.Zero;
                int           denominatorLeadingTerm = rLast.GetCoefficient(rLast.Degree);
                int           dltInverse             = field.Inverse(denominatorLeadingTerm);

                while (r.Degree >= rLast.Degree && !r.IsZero)
                {
                    int degreeDiff = r.Degree - rLast.Degree;
                    int scale      = field.Multiply(r.GetCoefficient(r.Degree), dltInverse);
                    q = q.AddOrSubtract(field.BuildMonomial(degreeDiff, scale));
                    r = r.AddOrSubtract(rLast.MultiplyByMonomial(degreeDiff, scale));
                }

                t = q.Multiply(tLast).AddOrSubtract(tLastLast);

                if (r.Degree >= rLast.Degree)
                {
                    // throw new IllegalStateException("Division algorithm failed to reduce polynomial?");
                    return(null);
                }
            }

            int sigmaTildeAtZero = t.GetCoefficient(0);

            if (sigmaTildeAtZero == 0)
            {
                // throw new ReedSolomonException("sigmaTilde(0) was zero");
                return(null);
            }

            int           inverse = field.Inverse(sigmaTildeAtZero);
            GenericGFPoly sigma   = t.Multiply(inverse);
            GenericGFPoly omega   = r.Multiply(inverse);

            return(new GenericGFPoly[] { sigma, omega });
        }