Поля Галуа

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Lab02_5GF_
{
    class GF
    {
        private byte binaryPolynom;

        public GF(byte input) =>
            binaryPolynom = input;

        public byte Polynom => binaryPolynom;

        static public GF operator +(GF left, GF right) => new GF((byte)(left.Polynom ^ right.Polynom));

        static public GF operator*(GF left, GF right)
        {
            var result = default(ushort);
            for (var i = 0; i < 8; i++)
                for (var j = 0; j < 8; j++)
                    result ^= (ushort)((left[i] & right[j]) << (i + j));

            return new GF((byte)DivisionRemainder(result,11));
        }

        static public ushort DivisionRemainder(ushort firstOperand, ushort secondOperand)
        {
            if (secondOperand == 0)
                throw new ArgumentException("secondOperand");

            if (firstOperand == 0)
                return 0;

            if (firstOperand == 1)
            {
                if (secondOperand == 1)
                    return 0;
                return 1;
            }

            var firstOperandMaxPower = getMaxPow(firstOperand);
            var secondOperandMaxPower = getMaxPow(secondOperand);

            while (firstOperandMaxPower >= secondOperandMaxPower)
            {
                firstOperand ^= (ushort)(secondOperand << (firstOperandMaxPower - secondOperandMaxPower));
                firstOperandMaxPower = getMaxPow(firstOperand);
            }

            return firstOperand;
        }

        static public byte getMaxPow(ushort num)
        {
            var numCopy = num;
            byte pow = 0;

            while(numCopy != 1)
            {
                numCopy >>= 1;
                pow++;
            }

            return pow;
        }


       public  static void modInverse(int a, int m)
        {
            int g = gcd(a, m);
            if (g != 1)
                Console.Write("Inverse doesn't exist");
            else
            {
                // If a and m are relatively
                // prime, then modulo inverse
                // is a^(m-2) mode m
                Console.Write("Modular multiplicative inverse is " +
                                                 power(a, m - 2, m));
            }
        }

        // To compute x^y under
        // modulo m
        static int power(int x, int y, int m)
        {
            if (y == 0)
                return 1;

            int p = power(x, y / 2, m) % m;
            p = (p * p) % m;

            if (y % 2 == 0)
                return p;
            else
                return (x * p) % m;
        }

        // Function to return
        // gcd of a and b
        static int gcd(int a, int b)
        {
            if (a == 0)
                return b;
            return gcd(b % a, a);
        }

        public int this[int index] => ((1 << index) & binaryPolynom) >> index;

        public override string ToString()
        {
            var GFInStr = string.Empty;

            for (int i = 7; i >= 0; i--)
            {
                if(this[i] != 0)
                    GFInStr += i == 0 ? $"1" : i > 1 ? $"x^{i}" : $"x";
                if (i != 0 && i!= 7) GFInStr += "+";
            }

            return GFInStr;
        }
    }
}