gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x0000000000004000000000000000000000000000000000000000000000000000 a = x²⁰⁶
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
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10010111101110011010111101101000001011001100100100010101011001011001100001100001011001111010111111001100100110100010110100100100000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011100011001010111100011011100001110101010110110011111110101110101010001010001110101000111100000101010110101110011101110110110000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111001100010110001001100000110001100011001111111011010100011100011001001001001100011011001001111011001111100011011000011111111000000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011011111000010011011101011001101000000011011111000001000101000000101000101101000010110011000100000011000101111010101011011100000000000000000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111110000011110101110010000011101010110000010110000100010011010110110000110101010100101101101011110000001100010010000110010101000000000000000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1100111110000110100101101110101011101001110010100110111000011101111100111001011111100010111100001001101000100110010000110001100000000000000000000000000000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10111100011011010001001011100111011010001001101111000101000001110110111001110111000100010011001100001100100100110100100111111100000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110111101100011100010101010011011111101111111101001111101101011010001001000111101000101110010011101010110111100101111101101110000000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10010010111111010111010001001011101011100110100001010111011001100010001011111111110110000111100011001111110001101010000100111000000000000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1011001001000011010001111111111101110000000110011011101110101001110111011001111011010111010111100101001100010111011011110101010000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 111100110011111100100000100101101100110011111010011000100011011000100011010111001100100100010011011010101011010011110011100011000000000000000000000000000000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1110001110001111110111001000101101101010011110111010001000010011101111011011000111101011000100100011001111100111100101000111100000000000000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1111011111101001000010010011111011010010101001101101011011100110110000101101100010010010101101000011110000011001011001110011000000000000000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11110000110101110111101000101011000100110000100101110001010100000011101110100000100001011000111101101001010100011100011010001000000000000000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1100001100000011101010001100010111100000100111100110100011010100001110010101101100000111101000010000000001100000111001011110000000000000000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100011011111011111110111000111110110111110101110001001100110111101010110101110110100011101101110011000101101111100110111001000000000000000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 100010011001001111110100111000111011101100001110010110010100001001111100111111000000110100111100011100010011111101111010111111000000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10000100100111100100011010101111010110101101010110100111111000010110000110011001011111011101011100101110111001001101100011011100000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001111010000101001000100011011010011001011000100101101010100111010110110101001110011100000000011001000101010011100111001001110000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101010101011001111101011000001010001111000001101101000000010101100101110110001100101111110101100111011100011110100010100000111000000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11000010110111100111100101100010000100001101001001010101001100111100010111101101110110001111011000010000111000000000010100011100000000000000000000000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1001000000101010111011010110000001101011011011011111100000010000100111011101011010110010000111110110101011010001001110001110000000000000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 110011101111011001001110001101110011101000100001010101010111100001001111001001110100110101101000011000101001111000001001111110000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1010010101010011001100000110010110001000101110111111100101010000011000101111111111010111111100001001101001100011111011010100000000000000000000 | - 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1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 101101100001100011000000101110010101111011010011011010111011110010001101011100111101110011001000111100001000011100001001101100000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 11111011100010000010111000011010100100010110111111000010000111001000001010000110110111100011111000101101100101000011111001000100000000000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 110000010101001111100110101110100001110000101101001000101011100100111010110110011011011110100111001011110110010010100011010110000000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 10101000111100110001000011100000101001001001101010000000101111110110111010010000010001110000110010010010100110110101110010100000000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 1100011001011111100011101010100101100101111111000001010000011011010001010100000111101001101101101110100110101100100101000110010000 | - 1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 110110000011010110010001110101110011100110001001111010101001100010010111000101011010011000010000111111100001100000101111011000 | - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0
c_quotient = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111101101000011111011101011001010101110001000111111110001110100001100110100011000 c_quotient = 0x00000000000000000000000000000000000000000001ed0fbacab88ff1d0cd18 c_quotient = x⁸⁰ + x⁷⁹ + x⁷⁸ + x⁷⁷ + x⁷⁵ + x⁷⁴ + x⁷² + x⁶⁷ + x⁶⁶ + x⁶⁵ + x⁶⁴ + x⁶³ + x⁶¹ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁵ + x⁵⁴ + x⁵¹ + x⁴⁹ + x⁴⁷ + x⁴⁵ + x⁴⁴ + x⁴³ + x³⁹ + x³⁵ + x³⁴ + x³³ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁴ + x²³ + x²² + x²⁰ + x¹⁵ + x¹⁴ + x¹¹ + x¹⁰ + x⁸ + x⁴ + x³
c_remainder = b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000110110000011010110010001110101110011100110001001111010101001100010010111000101011010011000010000111111100001100000101111011000 c_remainder = 0x00000000000000000000000000000000360d6475ce627aa625c569843f860bd8 c_remainder = x¹²⁵ + x¹²⁴ + x¹²² + x¹²¹ + x¹¹⁵ + x¹¹⁴ + x¹¹² + x¹¹⁰ + x¹⁰⁹ + x¹⁰⁶ + x¹⁰² + x¹⁰¹ + x¹⁰⁰ + x⁹⁸ + x⁹⁶ + x⁹⁵ + x⁹⁴ + x⁹¹ + x⁹⁰ + x⁸⁹ + x⁸⁶ + x⁸⁵ + x⁸¹ + x⁷⁸ + x⁷⁷ + x⁷⁶ + x⁷⁵ + x⁷³ + x⁷¹ + x⁶⁹ + x⁶⁶ + x⁶⁵ + x⁶¹ + x⁵⁸ + x⁵⁶ + x⁵⁵ + x⁵⁴ + x⁵⁰ + x⁴⁸ + x⁴⁶ + x⁴⁵ + x⁴³ + x⁴⁰ + x³⁹ + x³⁴ + x²⁹ + x²⁸ + x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²³ + x¹⁸ + x¹⁷ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁴ + x³