# GF(2^6) mod x^6 + x^3 + 1 (II)

## Stevie O

Polynomial info: g: x Algebraic: x^6 + x^3 + 1 Decimal: 73 Hex: 0x49 Degree: 6 '1' bits: 3 Is irreducible? True Cycle length: 9 g^0 = 0x1 1 [1] g^1 = 0x2 2 [x] g^2 = 0x4 4 [x^2] g^3 = 0x8 8 [x^3] g^4 = 0x10 16 [x^4] g^5 = 0x20 32 [x^5] g^6 = 0x9 9 [x^3 + 1] g^7 = 0x12 18 [x^4 + x] g^8 = 0x24 36 [x^5 + x^2] g^9 = 0x1 1 [1] Duplicate of g^0 Starting at x^2 + 1: a_0 = [x^2 + 1] a_1 = [x^3 + x] a_2 = [x^4 + x^2] a_3 = [x^5 + x^3] a_4 = [x^4 + x^3 + 1] a_5 = [x^5 + x^4 + x] a_6 = [x^5 + x^3 + x^2 + 1] a_7 = [x^4 + x + 1] a_8 = [x^5 + x^2 + x] a_9 = [x^2 + 1] Duplicate of a_0

Friday, 2 August 2019 16:02 GMT