gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0400000000000000000000000000000000000000000000000000000000000000 a = x²⁵⁰
b = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 b = 0x0000000000000000000000000000000065ee6bda0b324559661859ebf3268b49 b = x¹²⁶ + x¹²⁵ + x¹²² + x¹²⁰ + x¹¹⁹ + x¹¹⁸ + x¹¹⁷ + x¹¹⁵ + x¹¹⁴ + x¹¹³ + x¹¹⁰ + x¹⁰⁹ + x¹⁰⁷ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰³ + x¹⁰² + x¹⁰⁰ + x⁹⁹ + x⁹⁷ + x⁹¹ + x⁸⁹ + x⁸⁸ + x⁸⁵ + x⁸⁴ + x⁸¹ + x⁷⁸ + x⁷⁴ + x⁷² + x⁷⁰ + x⁶⁸ + x⁶⁷ + x⁶⁴ + x⁶² + x⁶¹ + x⁵⁸ + x⁵⁷ + x⁵² + x⁵¹ + x⁴⁶ + x⁴⁴ + x⁴³ + x⁴⁰ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³³ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁵ + x²⁴ + x²¹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹¹ + x⁹ + x⁸ + x⁶ + x³ + 1
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001011110111001101011110110100000101100110010010001010101100101100110000110000101100111101011111100110010011010001011010010010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101110001100101011110001101110000111010101011011001111111010111010101000101000111010100011110000010101011010111001110111011011000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11100110001011000100110000011000110001100111111101101010001110001100100100100110001101100100111101100111110001101100001111111100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101101111100001001101110101100110100000001101111100000100010100000010100010110100001011001100010000001100010111101010101101110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11111000001111010111001000001110101011000001011000010001001101011011000011010101010010110110101111000000110001001000011001010100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 110011111000011010010110111010101110100111001010011011100001110111110011100101111110001011110000100110100010011001000011000110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1000101101001000001010111101111111110101110111001001010111100111111101001110101000100100111011111000110101101010101100010100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100000010010100111111000110101111100011101110000001111101010101001110001101101010010111001110000110101100100111101001111101001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10010101111010100101111011000111101000100010100101101000001100010111101100001011001110110100111001100000000001001011001001101100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011110001101101000100101110011101101000100110111100010100000111011011100111011100010001001100110000110010010011010010011111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111011110110001110001010101001101111110111111110100111110110101101000100100011110100010111001001110101011011110010111110110111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001001011111101011101000100101110101110011010000101011101100110001000101111111111011000011110001100111111000110101000010011100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111000111000111111011100100010110110101001111011101000100001001110111101101100011110101100010010001100111110011110010100011110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1010000101001100001011001111110111110000011111001010001010000101110001100000010101100011000101110101011010101010000010111010100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11101100001011101011011001111100000101011011011111101111100010111101111001000000110110010110001000111100011100110100000001101000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100111111100100110000111001000000000111101001101100101001110010001001001110000011010101011010111011010001111100101011011111010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 110000110000001110101000110001011110000010011110011010001101010000111001010110110000011110100001000000000110000011100101111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100011110001010100101101110001011100101111100011101001100001001111110010010011101011010101001001110111101101001010101011111011000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10001001100100111111010011100011101110110000111001011001010000100111110011111100000011010011110001110001001111110111101011111100000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1000010010011110010001101010111101011010110101011010011111100001011000011001100101111101110101110010111011100100110110001101110000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100111101000010100100010001101101001100101100010010110101010011101011011010100111001110000000001100100010101001110011100100111000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10101010101100111110101100000101000111100000110110100000001010110010111011000110010111111010110011101110001111010001010000011100000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1100001011011110011110010110001000010000110100100101010100110011110001011110110111011000111101100001000011100000000001010001110000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100100000010101011101101011000000110101101101101111110000001000010011101110101101011001000011111011010101101000100111000111000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10110111111011000111010110101000111110100001001011100101010001001010001111001100000000111001000100011001001110000101110011100100000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1111100001100001010001000011100111011000111011001101111111101100110111111111100101100000100011011111111011101010100101001110110000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11001110111101100100111000110111001110100010000101010101011110000100111100100111010011010110100001100010100111100000100111111000000000000000000000000000000000000000000000000000000000000000000 | - 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c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011110110100001111101110101100101010111000100011111111000111010000110011010001100010011100010110010111010010111100001110111010 c_quotient = 0x000000000000000000000000000000001ed0fbacab88ff1d0cd189c5974bc3ba c_quotient = x¹²⁴ + x¹²³ + x¹²² + x¹²¹ + x¹¹⁹ + x¹¹⁸ + x¹¹⁶ + x¹¹¹ + x¹¹⁰ + x¹⁰⁹ + x¹⁰⁸ + x¹⁰⁷ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰³ + x¹⁰¹ + x⁹⁹ + x⁹⁸ + x⁹⁵ + x⁹³ + x⁹¹ + x⁸⁹ + x⁸⁸ + x⁸⁷ + x⁸³ + x⁷⁹ + x⁷⁸ + x⁷⁷ + x⁷⁶ + x⁷⁵ + x⁷⁴ + x⁷³ + x⁷² + x⁶⁸ + x⁶⁷ + x⁶⁶ + x⁶⁴ + x⁵⁹ + x⁵⁸ + x⁵⁵ + x⁵⁴ + x⁵² + x⁴⁸ + x⁴⁷ + x⁴³ + x⁴⁰ + x³⁹ + x³⁸ + x³⁴ + x³² + x³¹ + x²⁸ + x²⁶ + x²⁵ + x²⁴ + x²² + x¹⁹ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x⁹ + x⁸ + x⁷ + x⁵ + x⁴ + x³ + x
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101111101111000000000001100010000001101110011001001001100110011101110111100101110110110000111111001100101111010010111011101010 c_remainder = 0x000000000000000000000000000000002fbc006206e64999dde5db0fccbd2eea c_remainder = x¹²⁵ + x¹²³ + x¹²² + x¹²¹ + x¹²⁰ + x¹¹⁹ + x¹¹⁷ + x¹¹⁶ + x¹¹⁵ + x¹¹⁴ + x¹⁰² + x¹⁰¹ + x⁹⁷ + x⁹⁰ + x⁸⁹ + x⁸⁷ + x⁸⁶ + x⁸⁵ + x⁸² + x⁸¹ + x⁷⁸ + x⁷⁵ + x⁷² + x⁷¹ + x⁶⁸ + x⁶⁷ + x⁶⁴ + x⁶³ + x⁶² + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁶ + x⁵⁵ + x⁵⁴ + x⁵³ + x⁵⁰ + x⁴⁸ + x⁴⁷ + x⁴⁶ + x⁴⁴ + x⁴³ + x⁴¹ + x⁴⁰ + x³⁵ + x³⁴ + x³³ + x³² + x³¹ + x³⁰ + x²⁷ + x²⁶ + x²³ + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁶ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x⁷ + x⁶ + x⁵ + x³ + x