gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000100000100000001010001000100000101010101010001000101010000010000000000000000010000000001010000010101010000010001010101010001 a = 0x04101444155445410000401415411551 a = x¹²² + x¹¹⁶ + x¹⁰⁸ + x¹⁰⁶ + x¹⁰² + x⁹⁸ + x⁹² + x⁹⁰ + x⁸⁸ + x⁸⁶ + x⁸⁴ + x⁸² + x⁷⁸ + x⁷⁴ + x⁷² + x⁷⁰ + x⁶⁴ + x⁴⁶ + x³⁶ + x³⁴ + x²⁸ + x²⁶ + x²⁴ + x²² + x¹⁶ + x¹² + x¹⁰ + x⁸ + x⁶ + x⁴ + 1
b = b00000000000101010100010001010101010100000100000000010101000000000001000100000101000001000000010100000100000101010001000001000000 b = 0x00154455504015001105040504151040 b = x¹¹⁶ + x¹¹⁴ + x¹¹² + x¹¹⁰ + x¹⁰⁶ + x¹⁰² + x¹⁰⁰ + x⁹⁸ + x⁹⁶ + x⁹⁴ + x⁹² + x⁸⁶ + x⁷⁶ + x⁷⁴ + x⁷² + x⁶⁰ + x⁵⁶ + x⁵⁰ + x⁴⁸ + x⁴² + x³⁴ + x³² + x²⁶ + x²⁰ + x¹⁸ + x¹⁶ + x¹² + x⁶
100000100000001010001000100000101010101010001000101010000010000000000000000010000000001010000010101010000010001010101010001 | 101010100010001010101010100000100000000010101000000000001000100000101000001000000010100000100000101010001000001000000 - 101010100010001010101010100000100000000010101000000000001000100000101000001000000010100000100000101010001000001000000 | 1 --------------------------------------------------------------------------------------------------------------------------- | 1010000010000000100010000000001010101000100000101010001010100000101000001010000010101010100010000000001010000010101010001 | - 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 101010100010001010101010100000100000000010101000000000001000100000101000001000000010100000100000101010001000001000000 | 1 --------------------------------------------------------------------------------------------------------------------------- | 101010100010001000101000000010101000001010101010001000101000100010001000000010000010101010001010101000000000101010001 | - 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 0 - 101010100010001010101010100000100000000010101000000000001000100000101000001000000010100000100000101010001000001000000 | 1 --------------------------------------------------------------------------------------------------------------------------- | 10000010100010001000001000000010001000100000000010100000001010000000001010101010000010001000100010001 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001010001 c_quotient = 0x00000000000000000000000000000051 c_quotient = x⁶ + x⁴ + 1
c_remainder = b00000000000000000000000000010000010100010001000001000000010001000100000000010100000001010000000001010101010000010001000100010001 c_remainder = 0x00000010511040444014050055411111 c_remainder = x¹⁰⁰ + x⁹⁴ + x⁹² + x⁸⁸ + x⁸⁴ + x⁷⁸ + x⁷⁰ + x⁶⁶ + x⁶² + x⁵² + x⁵⁰ + x⁴² + x⁴⁰ + x³⁰ + x²⁸ + x²⁶ + x²⁴ + x²² + x¹⁶ + x¹² + x⁸ + x⁴ + 1