f = b0000000000000000111101111101100100100100100111111111001100111111 f = 0x0000f7d9249ff33f f = x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁶ + x³⁵ + x³² + x²⁹ + x²⁶ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1

v₀ = x⁰ (mod f)
v₀ = b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 v₀ = 0x000000000000000000000001 v₀ = 1
v₁ = x² (mod f)
v₁ = b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100 v₁ = 0x000000000000000000000004 v₁ = x²
v₂ = x⁴ (mod f)
v₂ = b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000 v₂ = 0x000000000000000000000010 v₂ = x⁴
v₃ = x⁶ (mod f)
v₃ = b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000 v₃ = 0x000000000000000000000040 v₃ = x⁶
v₄ = x⁸ (mod f)
v₄ = b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000 v₄ = 0x000000000000000000000100 v₄ = x⁸
v₅ = x¹⁰ (mod f)
v₅ = b000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000 v₅ = 0x000000000000000000000400 v₅ = x¹⁰
v₆ = x¹² (mod f)
v₆ = b000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000 v₆ = 0x000000000000000000001000 v₆ = x¹²
v₇ = x¹⁴ (mod f)
v₇ = b000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000 v₇ = 0x000000000000000000004000 v₇ = x¹⁴
v₈ = x¹⁶ (mod f)
v₈ = b000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000 v₈ = 0x000000000000000000010000 v₈ = x¹⁶
v₉ = x¹⁸ (mod f)
v₉ = b000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000 v₉ = 0x000000000000000000040000 v₉ = x¹⁸
v₁₀ = x²⁰ (mod f)
v₁₀ = b000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000 v₁₀ = 0x000000000000000000100000 v₁₀ = x²⁰
v₁₁ = x²² (mod f)
v₁₁ = b000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000 v₁₁ = 0x000000000000000000400000 v₁₁ = x²²
v₁₂ = x²⁴ (mod f)
v₁₂ = b000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000 v₁₂ = 0x000000000000000001000000 v₁₂ = x²⁴
v₁₃ = x²⁶ (mod f)
v₁₃ = b000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000 v₁₃ = 0x000000000000000004000000 v₁₃ = x²⁶
v₁₄ = x²⁸ (mod f)
v₁₄ = b000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000 v₁₄ = 0x000000000000000010000000 v₁₄ = x²⁸
v₁₅ = x³⁰ (mod f)
v₁₅ = b000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000 v₁₅ = 0x000000000000000040000000 v₁₅ = x³⁰
v₁₆ = x³² (mod f)
v₁₆ = b000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000 v₁₆ = 0x000000000000000100000000 v₁₆ = x³²
v₁₇ = x³⁴ (mod f)
v₁₇ = b000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000 v₁₇ = 0x000000000000000400000000 v₁₇ = x³⁴
v₁₈ = x³⁶ (mod f)
v₁₈ = b000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000 v₁₈ = 0x000000000000001000000000 v₁₈ = x³⁶
v₁₉ = x³⁸ (mod f)
v₁₉ = b000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000 v₁₉ = 0x000000000000004000000000 v₁₉ = x³⁸
v₂₀ = x⁴⁰ (mod f)
v₂₀ = b000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000 v₂₀ = 0x000000000000010000000000 v₂₀ = x⁴⁰
v₂₁ = x⁴² (mod f)
v₂₁ = b000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000 v₂₁ = 0x000000000000040000000000 v₂₁ = x⁴²
v₂₂ = x⁴⁴ (mod f)
v₂₂ = b000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000 v₂₂ = 0x000000000000100000000000 v₂₂ = x⁴⁴
v₂₃ = x⁴⁶ (mod f)
v₂₃ = b000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000 v₂₃ = 0x000000000000400000000000 v₂₃ = x⁴⁶
v₂₄ = x⁴⁸ (mod f)
v₂₄ = b000000000000000000000000000000000000000000000000000110000110101101101101101000000001010101000001 v₂₄ = 0x000000000000186b6da01541 v₂₄ = x⁴⁴ + x⁴³ + x³⁸ + x³⁷ + x³⁵ + x³³ + x³² + x³⁰ + x²⁹ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²¹ + x¹² + x¹⁰ + x⁸ + x⁶ + 1
v₂₅ = x⁵⁰ (mod f)
v₂₅ = b000000000000000000000000000000000000000000000000011000011010110110110110100000000101010100000100 v₂₅ = 0x00000000000061adb6805504 v₂₅ = x⁴⁶ + x⁴⁵ + x⁴⁰ + x³⁹ + x³⁷ + x³⁵ + x³⁴ + x³² + x³¹ + x²⁹ + x²⁸ + x²⁶ + x²⁵ + x²³ + x¹⁴ + x¹² + x¹⁰ + x⁸ + x²
v₂₆ = x⁵² (mod f)
v₂₆ = b000000000000000000000000000000000000000000000000011010010000010010010011001111101011001001101110 v₂₆ = 0x0000000000006904933eb26e v₂₆ = x⁴⁶ + x⁴⁵ + x⁴³ + x⁴⁰ + x³⁴ + x³¹ + x²⁸ + x²⁵ + x²⁴ + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹² + x⁹ + x⁶ + x⁵ + x³ + x² + x
v₂₇ = x⁵⁴ (mod f)
v₂₇ = b000000000000000000000000000000000000000000000000010010111010000000000101110001010010111111000110 v₂₇ = 0x0000000000004ba005c52fc6 v₂₇ = x⁴⁶ + x⁴³ + x⁴¹ + x⁴⁰ + x³⁹ + x³⁷ + x²⁶ + x²⁴ + x²³ + x²² + x¹⁸ + x¹⁶ + x¹³ + x¹¹ + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁶ + x² + x
v₂₈ = x⁵⁶ (mod f)
v₂₈ = b000000000000000000000000000000000000000000000000001101101110101101111010101101001010101001011001 v₂₈ = 0x00000000000036eb7ab4aa59 v₂₈ = x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³³ + x³² + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²⁵ + x²³ + x²¹ + x²⁰ + x¹⁸ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁶ + x⁴ + x³ + 1
v₂₉ = x⁵⁸ (mod f)
v₂₉ = b000000000000000000000000000000000000000000000000001011000111010011001110010011010101101001011011 v₂₉ = 0x0000000000002c74ce4d5a5b v₂₉ = x⁴⁵ + x⁴³ + x⁴² + x³⁸ + x³⁷ + x³⁶ + x³⁴ + x³¹ + x³⁰ + x²⁷ + x²⁶ + x²⁵ + x²² + x¹⁹ + x¹⁸ + x¹⁶ + x¹⁴ + x¹² + x¹¹ + x⁹ + x⁶ + x⁴ + x³ + x + 1
v₃₀ = x⁶⁰ (mod f)
v₃₀ = b000000000000000000000000000000000000000000000000010001100000101000011101101010101001101001010011 v₃₀ = 0x000000000000460a1daa9a53 v₃₀ = x⁴⁶ + x⁴² + x⁴¹ + x³⁵ + x³³ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²¹ + x¹⁹ + x¹⁷ + x¹⁵ + x¹² + x¹¹ + x⁹ + x⁶ + x⁴ + x + 1
v₃₁ = x⁶² (mod f)
v₃₁ = b000000000000000000000000000000000000000000000000000000000100001100011011000010100111110000001101 v₃₁ = 0x00000000000000431b0a7c0d v₃₁ = x³⁸ + x³³ + x³² + x²⁸ + x²⁷ + x²⁵ + x²⁴ + x¹⁹ + x¹⁷ + x¹⁴ + x¹³ + x¹² + x¹¹ + x¹⁰ + x³ + x² + 1
v₃₂ = x⁶⁴ (mod f)
v₃₂ = b000000000000000000000000000000000000000000000000000000010000110001101100001010011111000000110100 v₃₂ = 0x000000000000010c6c29f034 v₃₂ = x⁴⁰ + x³⁵ + x³⁴ + x³⁰ + x²⁹ + x²⁷ + x²⁶ + x²¹ + x¹⁹ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁵ + x⁴ + x²
v₃₃ = x⁶⁶ (mod f)
v₃₃ = b000000000000000000000000000000000000000000000000000001000011000110110000101001111100000011010000 v₃₃ = 0x0000000000000431b0a7c0d0 v₃₃ = x⁴² + x³⁷ + x³⁶ + x³² + x³¹ + x²⁹ + x²⁸ + x²³ + x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x⁷ + x⁶ + x⁴
v₃₄ = x⁶⁸ (mod f)
v₃₄ = b000000000000000000000000000000000000000000000000000100001100011011000010100111110000001101000000 v₃₄ = 0x00000000000010c6c29f0340 v₃₄ = x⁴⁴ + x³⁹ + x³⁸ + x³⁴ + x³³ + x³¹ + x³⁰ + x²⁵ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x⁹ + x⁸ + x⁶
v₃₅ = x⁷⁰ (mod f)
v₃₅ = b000000000000000000000000000000000000000000000000010000110001101100001010011111000000110100000000 v₃₅ = 0x000000000000431b0a7c0d00 v₃₅ = x⁴⁶ + x⁴¹ + x⁴⁰ + x³⁶ + x³⁵ + x³³ + x³² + x²⁷ + x²⁵ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹¹ + x¹⁰ + x⁸
v₃₆ = x⁷² (mod f)
v₃₆ = b000000000000000000000000000000000000000000000000000101000000011101000100010100000010000101000001 v₃₆ = 0x000000000000140744502141 v₃₆ = x⁴⁴ + x⁴² + x³⁴ + x³³ + x³² + x³⁰ + x²⁶ + x²² + x²⁰ + x¹³ + x⁸ + x⁶ + 1
v₃₇ = x⁷⁴ (mod f)
v₃₇ = b000000000000000000000000000000000000000000000000010100000001110100010001010000001000010100000100 v₃₇ = 0x000000000000501d11408504 v₃₇ = x⁴⁶ + x⁴⁴ + x³⁶ + x³⁵ + x³⁴ + x³² + x²⁸ + x²⁴ + x²² + x¹⁵ + x¹⁰ + x⁸ + x²
v₃₈ = x⁷⁶ (mod f)
v₃₈ = b000000000000000000000000000000000000000000000000010110000001111100101000101000100000000101010001 v₃₈ = 0x000000000000581f28a20151 v₃₈ = x⁴⁶ + x⁴⁴ + x⁴³ + x³⁶ + x³⁵ + x³⁴ + x³³ + x³² + x²⁹ + x²⁷ + x²³ + x²¹ + x¹⁷ + x⁸ + x⁶ + x⁴ + 1
v₃₉ = x⁷⁸ (mod f)
v₃₉ = b000000000000000000000000000000000000000000000000011110000001011111001111001010000001000000000101 v₃₉ = 0x0000000000007817cf281005 v₃₉ = x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴³ + x³⁶ + x³⁴ + x³³ + x³² + x³¹ + x³⁰ + x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²¹ + x¹⁹ + x¹² + x² + 1
v₄₀ = x⁸⁰ (mod f)
v₄₀ = b000000000000000000000000000000000000000000000000000011111110110101110101100111111010011001101010 v₄₀ = 0x0000000000000fed759fa66a v₄₀ = x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³² + x³⁰ + x²⁹ + x²⁸ + x²⁶ + x²⁴ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹⁰ + x⁹ + x⁶ + x⁵ + x³ + x
v₄₁ = x⁸² (mod f)
v₄₁ = b000000000000000000000000000000000000000000000000001111111011010111010110011111101001100110101000 v₄₁ = 0x0000000000003fb5d67e99a8 v₄₁ = x⁴⁵ + x⁴⁴ + x⁴³ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁷ + x³⁶ + x³⁴ + x³² + x³¹ + x³⁰ + x²⁸ + x²⁶ + x²⁵ + x²² + x²¹ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹² + x¹¹ + x⁸ + x⁷ + x⁵ + x³
v₄₂ = x⁸⁴ (mod f)
v₄₂ = b000000000000000000000000000000000000000000000000000010010000111001111101011001011001010110011111 v₄₂ = 0x000000000000090e7d65959f v₄₂ = x⁴³ + x⁴⁰ + x³⁵ + x³⁴ + x³³ + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²² + x²¹ + x¹⁸ + x¹⁶ + x¹⁵ + x¹² + x¹⁰ + x⁸ + x⁷ + x⁴ + x³ + x² + x + 1
v₄₃ = x⁸⁶ (mod f)
v₄₃ = b000000000000000000000000000000000000000000000000001001000011100111110101100101100101011001111100 v₄₃ = 0x0000000000002439f596567c v₄₃ = x⁴⁵ + x⁴² + x³⁷ + x³⁶ + x³⁵ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁶ + x²⁴ + x²³ + x²⁰ + x¹⁸ + x¹⁷ + x¹⁴ + x¹² + x¹⁰ + x⁹ + x⁶ + x⁵ + x⁴ + x³ + x²
v₄₄ = x⁸⁸ (mod f)
v₄₄ = b000000000000000000000000000000000000000000000000011001110011111011110010110001101010101011001111 v₄₄ = 0x000000000000673ef2c6aacf v₄₄ = x⁴⁶ + x⁴⁵ + x⁴² + x⁴¹ + x⁴⁰ + x³⁷ + x³⁶ + x³⁵ + x³⁴ + x³³ + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁵ + x²³ + x²² + x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁷ + x⁶ + x³ + x² + x + 1
v₄₅ = x⁹⁰ (mod f)
v₄₅ = b000000000000000000000000000000000000000000000000011100110100100110000010001001010100110101000010 v₄₅ = 0x000000000000734982254d42 v₄₅ = x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴¹ + x⁴⁰ + x³⁸ + x³⁵ + x³² + x³¹ + x²⁵ + x²¹ + x¹⁸ + x¹⁶ + x¹⁴ + x¹¹ + x¹⁰ + x⁸ + x⁶ + x
v₄₆ = x⁹² (mod f)
v₄₆ = b000000000000000000000000000000000000000000000000001000101001010001000001101010101101001101110110 v₄₆ = 0x000000000000229441aad376 v₄₆ = x⁴⁵ + x⁴¹ + x³⁹ + x³⁶ + x³⁴ + x³⁰ + x²⁴ + x²³ + x²¹ + x¹⁹ + x¹⁷ + x¹⁵ + x¹⁴ + x¹² + x⁹ + x⁸ + x⁶ + x⁵ + x⁴ + x² + x

Q = 00000000000000000000000000000000000000000000001 00000000000000000000000000000000000000000000100 00000000000000000000000000000000000000000010000 00000000000000000000000000000000000000001000000 00000000000000000000000000000000000000100000000 00000000000000000000000000000000000010000000000 00000000000000000000000000000000001000000000000 00000000000000000000000000000000100000000000000 00000000000000000000000000000010000000000000000 00000000000000000000000000001000000000000000000 00000000000000000000000000100000000000000000000 00000000000000000000000010000000000000000000000 00000000000000000000001000000000000000000000000 00000000000000000000100000000000000000000000000 00000000000000000010000000000000000000000000000 00000000000000001000000000000000000000000000000 00000000000000100000000000000000000000000000000 00000000000010000000000000000000000000000000000 00000000001000000000000000000000000000000000000 00000000100000000000000000000000000000000000000 00000010000000000000000000000000000000000000000 00001000000000000000000000000000000000000000000 00100000000000000000000000000000000000000000000 10000000000000000000000000000000000000000000000 00110000110101101101101101000000001010101000001 11000011010110110110110100000000101010100000100 11010010000010010010011001111101011001001101110 10010111010000000000101110001010010111111000110 01101101110101101111010101101001010101001011001 01011000111010011001110010011010101101001011011 10001100000101000011101101010101001101001010011 00000000100001100011011000010100111110000001101 00000010000110001101100001010011111000000110100 00001000011000110110000101001111100000011010000 00100001100011011000010100111110000001101000000 10000110001101100001010011111000000110100000000 00101000000011101000100010100000010000101000001 10100000001110100010001010000001000010100000100 10110000001111100101000101000100000000101010001 11110000001011111001111001010000001000000000101 00011111110110101110101100111111010011001101010 01111111011010111010110011111101001100110101000 00010010000111001111101011001011001010110011111 01001000011100111110101100101100101011001111100 11001110011111011110010110001101010101011001111 11100110100100110000010001001010100110101000010 01000101001010001000001101010101101001101110110

I = 00000000000000000000000000000000000000000000001 00000000000000000000000000000000000000000000010 00000000000000000000000000000000000000000000100 00000000000000000000000000000000000000000001000 00000000000000000000000000000000000000000010000 00000000000000000000000000000000000000000100000 00000000000000000000000000000000000000001000000 00000000000000000000000000000000000000010000000 00000000000000000000000000000000000000100000000 00000000000000000000000000000000000001000000000 00000000000000000000000000000000000010000000000 00000000000000000000000000000000000100000000000 00000000000000000000000000000000001000000000000 00000000000000000000000000000000010000000000000 00000000000000000000000000000000100000000000000 00000000000000000000000000000001000000000000000 00000000000000000000000000000010000000000000000 00000000000000000000000000000100000000000000000 00000000000000000000000000001000000000000000000 00000000000000000000000000010000000000000000000 00000000000000000000000000100000000000000000000 00000000000000000000000001000000000000000000000 00000000000000000000000010000000000000000000000 00000000000000000000000100000000000000000000000 00000000000000000000001000000000000000000000000 00000000000000000000010000000000000000000000000 00000000000000000000100000000000000000000000000 00000000000000000001000000000000000000000000000 00000000000000000010000000000000000000000000000 00000000000000000100000000000000000000000000000 00000000000000001000000000000000000000000000000 00000000000000010000000000000000000000000000000 00000000000000100000000000000000000000000000000 00000000000001000000000000000000000000000000000 00000000000010000000000000000000000000000000000 00000000000100000000000000000000000000000000000 00000000001000000000000000000000000000000000000 00000000010000000000000000000000000000000000000 00000000100000000000000000000000000000000000000 00000001000000000000000000000000000000000000000 00000010000000000000000000000000000000000000000 00000100000000000000000000000000000000000000000 00001000000000000000000000000000000000000000000 00010000000000000000000000000000000000000000000 00100000000000000000000000000000000000000000000 01000000000000000000000000000000000000000000000 10000000000000000000000000000000000000000000000

M = 00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000110 00000000000000000000000000000000000000000010100 00000000000000000000000000000000000000001001000 00000000000000000000000000000000000000100010000 00000000000000000000000000000000000010000100000 00000000000000000000000000000000001000001000000 00000000000000000000000000000000100000010000000 00000000000000000000000000000010000000100000000 00000000000000000000000000001000000001000000000 00000000000000000000000000100000000010000000000 00000000000000000000000010000000000100000000000 00000000000000000000001000000000001000000000000 00000000000000000000100000000000010000000000000 00000000000000000010000000000000100000000000000 00000000000000001000000000000001000000000000000 00000000000000100000000000000010000000000000000 00000000000010000000000000000100000000000000000 00000000001000000000000000001000000000000000000 00000000100000000000000000010000000000000000000 00000010000000000000000000100000000000000000000 00001000000000000000000001000000000000000000000 00100000000000000000000010000000000000000000000 10000000000000000000000100000000000000000000000 00110000110101101101100101000000001010101000001 11000011010110110110100100000000101010100000100 11010010000010010010111001111101011001001101110 10010111010000000001101110001010010111111000110 01101101110101101101010101101001010101001011001 01011000111010011101110010011010101101001011011 10001100000101001011101101010101001101001010011 00000000100001110011011000010100111110000001101 00000010000110101101100001010011111000000110100 00001000011001110110000101001111100000011010000 00100001100001011000010100111110000001101000000 10000110001001100001010011111000000110100000000 00101000001011101000100010100000010000101000001 10100000011110100010001010000001000010100000100 10110000101111100101000101000100000000101010001 11110001001011111001111001010000001000000000101 00011101110110101110101100111111010011001101010 01111011011010111010110011111101001100110101000 00011010000111001111101011001011001010110011111 01011000011100111110101100101100101011001111100 11101110011111011110010110001101010101011001111 10100110100100110000010001001010100110101000010 11000101001010001000001101010101101001101110110

nv₀ = b000000000000000000000000000000000000000000000000010000110000110000001110100101100010101100011000 nv₀ = 0x000000000000430c0e962b18 nv₀ = x⁴⁶ + x⁴¹ + x⁴⁰ + x³⁵ + x³⁴ + x²⁷ + x²⁶ + x²⁵ + x²³ + x²⁰ + x¹⁸ + x¹⁷ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁴ + x³
nv₁ = b000000000000000000000000000000000000000000000000001000101010001100101010101101010001000010010010 nv₁ = 0x00000000000022a32ab51092 nv₁ = x⁴⁵ + x⁴¹ + x³⁹ + x³⁷ + x³³ + x³² + x²⁹ + x²⁷ + x²⁵ + x²³ + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹² + x⁷ + x⁴ + x
nv₂ = b000000000000000000000000000000000000000000000000000100011011101100010010111000110111101000001100 nv₂ = 0x00000000000011bb12e37a0c nv₂ = x⁴⁴ + x⁴⁰ + x³⁹ + x³⁷ + x³⁶ + x³⁵ + x³³ + x³² + x²⁸ + x²⁵ + x²³ + x²² + x²¹ + x¹⁷ + x¹⁶ + x¹⁴ + x¹³ + x¹² + x¹¹ + x⁹ + x³ + x²
nv₃ = b000000000000000000000000000000000000000000000000000010001011001011101101101010110001011000000000 nv₃ = 0x00000000000008b2edab1600 nv₃ = x⁴³ + x³⁹ + x³⁷ + x³⁶ + x³³ + x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²¹ + x¹⁹ + x¹⁷ + x¹⁶ + x¹² + x¹⁰ + x⁹
nv₄ = b000000000000000000000000000000000000000000000000000001111001111000100100100010101110100111101100 nv₄ = 0x000000000000079e248ae9ec nv₄ = x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁶ + x³⁵ + x³⁴ + x³³ + x²⁹ + x²⁶ + x²³ + x¹⁹ + x¹⁷ + x¹⁵ + x¹⁴ + x¹³ + x¹¹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x²
nv₅ = b000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 nv₅ = 0x000000000000000000000001 nv₅ = 1

kf_o = b0000000000000000111101111101100100100100100111111111001100111111 kf_o = 0x0000f7d9249ff33f kf_o = x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁶ + x³⁵ + x³² + x²⁹ + x²⁶ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1

nv₀ = b0000000000000000010000110000110000001110100101100010101100011000 nv₀ = 0x0000430c0e962b18 nv₀ = x⁴⁶ + x⁴¹ + x⁴⁰ + x³⁵ + x³⁴ + x²⁷ + x²⁶ + x²⁵ + x²³ + x²⁰ + x¹⁸ + x¹⁷ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁴ + x³

New factor (nf) = f/gcd(f,nv₀)

nf = b0000000000000000000000001100011101000000110100011000111011010101 nf = 0x000000c740d18ed5 nf = x³⁹ + x³⁸ + x³⁴ + x³³ + x³² + x³⁰ + x²³ + x²² + x²⁰ + x¹⁶ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁷ + x⁶ + x⁴ + x² + 1
Search though known factors (kf) for which (nf) factors evenly

kf₀ = b0000000000000000111101111101100100100100100111111111001100111111 kf₀ = 0x0000f7d9249ff33f kf₀ = x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁶ + x³⁵ + x³² + x²⁹ + x²⁶ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1
t = kf₀/nf

t_remainder = b0000000000000000000000000000000000000000000000000000000000000000 t_remainder = 0x0000000000000000 t_remainder = 0

t_remainder == 0, nf is a factor of kf₀

kf₀ = nf // Replace kf₀ with nf
kf₁ = t_quotient // Append t_quotient to known factors list

t_quotient = b0000000000000000000000000000000000000000000000000000000101000011 t_quotient = 0x0000000000000143 t_quotient = x⁸ + x⁶ + x + 1

nv₁ = b0000000000000000001000101010001100101010101101010001000010010010 nv₁ = 0x000022a32ab51092 nv₁ = x⁴⁵ + x⁴¹ + x³⁹ + x³⁷ + x³³ + x³² + x²⁹ + x²⁷ + x²⁵ + x²³ + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹² + x⁷ + x⁴ + x

New factor (nf) = f/gcd(f,nv₁)

nf = b0000000000000000000000000000000000000000001001111000101010011001 nf = 0x0000000000278a99 nf = x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁴ + x³ + 1
Search though known factors (kf) for which (nf) factors evenly

kf₀ = b0000000000000000000000001100011101000000110100011000111011010101 kf₀ = 0x000000c740d18ed5 kf₀ = x³⁹ + x³⁸ + x³⁴ + x³³ + x³² + x³⁰ + x²³ + x²² + x²⁰ + x¹⁶ + x¹⁵ + x¹¹ + x¹⁰ + x⁹ + x⁷ + x⁶ + x⁴ + x² + 1
t = kf₀/nf

t_remainder = b0000000000000000000000000000000000000000000000000000000000000000 t_remainder = 0x0000000000000000 t_remainder = 0

t_remainder == 0, nf is a factor of kf₀

kf₀ = nf // Replace kf₀ with nf
kf₂ = t_quotient // Append t_quotient to known factors list

t_quotient = b0000000000000000000000000000000000000000000001101010101111101101 t_quotient = 0x000000000006abed t_quotient = x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + 1

nv₂ = b0000000000000000000100011011101100010010111000110111101000001100 nv₂ = 0x000011bb12e37a0c nv₂ = x⁴⁴ + x⁴⁰ + x³⁹ + x³⁷ + x³⁶ + x³⁵ + x³³ + x³² + x²⁸ + x²⁵ + x²³ + x²² + x²¹ + x¹⁷ + x¹⁶ + x¹⁴ + x¹³ + x¹² + x¹¹ + x⁹ + x³ + x²

New factor (nf) = f/gcd(f,nv₂)

nf = b0000000000000000000000000000000000000000000000000000000011000001 nf = 0x00000000000000c1 nf = x⁷ + x⁶ + 1
Search though known factors (kf) for which (nf) factors evenly

kf₀ = b0000000000000000000000000000000000000000001001111000101010011001 kf₀ = 0x0000000000278a99 kf₀ = x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁴ + x³ + 1
t = kf₀/nf

t_remainder = b0000000000000000000000000000000000000000000000000000000000001100 t_remainder = 0x000000000000000c t_remainder = x³ + x²

t_remainder != 0, nf is not a factor.

kf₁ = b0000000000000000000000000000000000000000000000000000000101000011 kf₁ = 0x0000000000000143 kf₁ = x⁸ + x⁶ + x + 1
t = kf₁/nf

t_remainder = b0000000000000000000000000000000000000000000000000000000000000000 t_remainder = 0x0000000000000000 t_remainder = 0

t_remainder == 0, nf is a factor of kf₁

kf₁ = nf // Replace kf₁ with nf
kf₃ = t_quotient // Append t_quotient to known factors list

t_quotient = b0000000000000000000000000000000000000000000000000000000000000011 t_quotient = 0x0000000000000003 t_quotient = x + 1

nv₃ = b0000000000000000000010001011001011101101101010110001011000000000 nv₃ = 0x000008b2edab1600 nv₃ = x⁴³ + x³⁹ + x³⁷ + x³⁶ + x³³ + x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁶ + x²⁴ + x²³ + x²¹ + x¹⁹ + x¹⁷ + x¹⁶ + x¹² + x¹⁰ + x⁹

New factor (nf) = f/gcd(f,nv₃)

nf = b0000000000000000000000000000000000001111010011001101011001101001 nf = 0x000000000f4cd669 nf = x²⁷ + x²⁶ + x²⁵ + x²⁴ + x²² + x¹⁹ + x¹⁸ + x¹⁵ + x¹⁴ + x¹² + x¹⁰ + x⁹ + x⁶ + x⁵ + x³ + 1
Search though known factors (kf) for which (nf) factors evenly

t_remainder = b0000000000000000000000000000000000000000001001111000101010011001 t_remainder = 0x0000000000278a99 t_remainder = x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁴ + x³ + 1

t_remainder != 0, nf is not a factor.

kf₁ = b0000000000000000000000000000000000000000000000000000000011000001 kf₁ = 0x00000000000000c1 kf₁ = x⁷ + x⁶ + 1
t = kf₁/nf

t_remainder = b0000000000000000000000000000000000000000000000000000000011000001 t_remainder = 0x00000000000000c1 t_remainder = x⁷ + x⁶ + 1

t_remainder != 0, nf is not a factor.

kf₂ = b0000000000000000000000000000000000000000000001101010101111101101 kf₂ = 0x000000000006abed kf₂ = x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + 1
t = kf₂/nf

t_remainder = b0000000000000000000000000000000000000000000001101010101111101101 t_remainder = 0x000000000006abed t_remainder = x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + 1

t_remainder != 0, nf is not a factor.

kf₃ = b0000000000000000000000000000000000000000000000000000000000000011 kf₃ = 0x0000000000000003 kf₃ = x + 1
t = kf₃/nf

t_remainder = b0000000000000000000000000000000000000000000000000000000000000011 t_remainder = 0x0000000000000003 t_remainder = x + 1

t_remainder != 0, nf is not a factor.

nv₄ = b0000000000000000000001111001111000100100100010101110100111101100 nv₄ = 0x0000079e248ae9ec nv₄ = x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁶ + x³⁵ + x³⁴ + x³³ + x²⁹ + x²⁶ + x²³ + x¹⁹ + x¹⁷ + x¹⁵ + x¹⁴ + x¹³ + x¹¹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x²

New factor (nf) = f/gcd(f,nv₄)

nf = b0000000000000000000000000000000000000000000000000000001110010011 nf = 0x0000000000000393 nf = x⁹ + x⁸ + x⁷ + x⁴ + x + 1
Search though known factors (kf) for which (nf) factors evenly

t_remainder = b0000000000000000000000000000000000000000000000000000000010000000 t_remainder = 0x0000000000000080 t_remainder = x⁷

t_remainder != 0, nf is not a factor.

kf₁ = b0000000000000000000000000000000000000000000000000000000011000001 kf₁ = 0x00000000000000c1 kf₁ = x⁷ + x⁶ + 1
t = kf₁/nf

t_remainder = b0000000000000000000000000000000000000000000000000000000011000001 t_remainder = 0x00000000000000c1 t_remainder = x⁷ + x⁶ + 1

t_remainder = b0000000000000000000000000000000000000000000000000000000101110001 t_remainder = 0x0000000000000171 t_remainder = x⁸ + x⁶ + x⁵ + x⁴ + 1

t_remainder != 0, nf is not a factor.

kf₃ = b0000000000000000000000000000000000000000000000000000000000000011 kf₃ = 0x0000000000000003 kf₃ = x + 1
t = kf₃/nf

t_remainder = b0000000000000000000000000000000000000000000000000000000000000011 t_remainder = 0x0000000000000003 t_remainder = x + 1

t_remainder != 0, nf is not a factor.

kf₀ = b0000000000000000000000000000000000000000001001111000101010011001 kf₀ = 0x0000000000278a99 kf₀ = x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁴ + x³ + 1
kf₁ = b0000000000000000000000000000000000000000000000000000000011000001 kf₁ = 0x00000000000000c1 kf₁ = x⁷ + x⁶ + 1
kf₂ = b0000000000000000000000000000000000000000000001101010101111101101 kf₂ = 0x000000000006abed kf₂ = x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + 1
kf₃ = b0000000000000000000000000000000000000000000000000000000000000011 kf₃ = 0x0000000000000003 kf₃ = x + 1

f = (b1001111000101010011001)(b11000001)(b1101010101111101101)(b11) f = (0x278a99)(0xc1)(0x6abed)(0x3) f = (x²¹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹¹ + x⁹ + x⁷ + x⁴ + x³ + 1)(x⁷ + x⁶ + 1)(x¹⁸ + x¹⁷ + x¹⁵ + x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x⁵ + x³ + x² + 1)(x + 1)

gf(2) Berlekamp Algorithm