// this method has been added by Sebastien ROBERT
        // this implementation makes the mathematician-friendly approach programmer-friendly
        public byte[] EncodeEx(byte[] toEncode, int ecBytes)
        {
            if (ecBytes == 0)
            {
                throw new ArgumentException("No error correction bytes");
            }

            int dataBytes = toEncode.Length - ecBytes;

            if (dataBytes <= 0)
            {
                throw new ArgumentException("No data bytes provided");
            }

            GenericGFPoly generator = BuildGenerator(ecBytes);

            int[] infoCoefficients = toEncode.Select(x => (int)x).ToArray();

            var info = new GenericGFPoly(field, infoCoefficients);

            info = info.MultiplyByMonomial(ecBytes, 1);

            GenericGFPoly remainder = info.Divide(generator)[1];

            int[] coefficients        = remainder.Coefficients;
            int   numZeroCoefficients = ecBytes - coefficients.Length;

            return(Enumerable.Repeat <byte>(0, numZeroCoefficients)
                   .Concat(coefficients.Select(x => (byte)x))
                   .ToArray());
        }
        public void Encode(int[] toEncode, int ecBytes)
        {
            if (ecBytes == 0)
            {
                throw new ArgumentException("No error correction bytes");
            }

            int dataBytes = toEncode.Length - ecBytes;

            if (dataBytes <= 0)
            {
                throw new ArgumentException("No data bytes provided");
            }

            GenericGFPoly generator        = BuildGenerator(ecBytes);
            var           infoCoefficients = new int[dataBytes];

            Array.Copy(toEncode, 0, infoCoefficients, 0, dataBytes);

            var info = new GenericGFPoly(field, infoCoefficients);

            info = info.MultiplyByMonomial(ecBytes, 1);

            GenericGFPoly remainder = info.Divide(generator)[1];

            int[] coefficients        = remainder.Coefficients;
            int   numZeroCoefficients = ecBytes - coefficients.Length;

            for (var i = 0; i < numZeroCoefficients; i++)
            {
                toEncode[dataBytes + i] = 0;
            }

            Array.Copy(coefficients, 0, toEncode, dataBytes + numZeroCoefficients, coefficients.Length);
        }