本原多项式列表

从这里薅一份列表
http://www.partow.net/programming/polynomials/index.html

https://en.wikipedia.org/wiki/Primitive_polynomial_(field_theory)

举例

x^5 + x^2 + 1
x^5 + x^4 + x^2 + x^1 + 1
x^5 + x^4 + x^3 + x^2 + 1

都是\(GF(2^5)\)的本原多项式

列表

The following is a list of primitive irreducible polynomials for generating elements of a binary extension field GF(2m) from a base finite field. The list contains polynomials of degree 2 to 32.

x^2 + x^1 + 1
x^3 + x^1 + 1
x^4 + x^1 + 1
x^5 + x^2 + 1
x^5 + x^4 + x^2 + x^1 + 1
x^5 + x^4 + x^3 + x^2 + 1
x^6 + x^1 + 1
x^6 + x^5 + x^2 + x^1 + 1
x^6 + x^5 + x^3 + x^2 + 1
x^7 + x^1 + 1
x^7 + x^3 + 1
x^7 + x^3 + x^2 + x^1 + 1
x^7 + x^4 + x^3 + x^2 + 1
x^7 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^7 + x^6 + x^3 + x^1 + 1
x^7 + x^6 + x^4 + x^2 + 1
x^7 + x^6 + x^5 + x^2 + 1
x^7 + x^6 + x^5 + x^4 + x^2 + x^1 + 1
x^8 + x^4 + x^3 + x^2 + 1
x^8 + x^5 + x^3 + x^1 + 1
x^8 + x^6 + x^4 + x^3 + x^2 + x^1 + 1
x^8 + x^6 + x^5 + x^1 + 1
x^8 + x^6 + x^5 + x^2 + 1
x^8 + x^6 + x^5 + x^3 + 1
x^8 + x^7 + x^6 + x^1 + 1
x^8 + x^7 + x^6 + x^5 + x^2 + x^1 + 1
x^9 + x^4 + 1
x^9 + x^5 + x^3 + x^2 + 1
x^9 + x^6 + x^4 + x^3 + 1
x^9 + x^6 + x^5 + x^3 + x^2 + x^1 + 1
x^9 + x^6 + x^5 + x^4 + x^2 + x^1 + 1
x^9 + x^7 + x^6 + x^4 + x^3 + x^1 + 1
x^9 + x^8 + x^4 + x^1 + 1
x^9 + x^8 + x^5 + x^4 + 1
x^9 + x^8 + x^6 + x^5 + 1
x^9 + x^8 + x^6 + x^5 + x^3 + x^1 + 1
x^9 + x^8 + x^7 + x^2 + 1
x^9 + x^8 + x^7 + x^3 + x^2 + x^1 + 1
x^9 + x^8 + x^7 + x^6 + x^5 + x^1 + 1
x^9 + x^8 + x^7 + x^6 + x^5 + x^3 + 1
x^10 + x^3 + 1
x^10 + x^4 + x^3 + x^1 + 1
x^10 + x^6 + x^5 + x^3 + x^2 + x^1 + 1
x^10 + x^8 + x^3 + x^2 + 1
x^10 + x^8 + x^4 + x^3 + 1
x^10 + x^8 + x^5 + x^1 + 1
x^10 + x^8 + x^5 + x^4 + 1
x^10 + x^8 + x^7 + x^6 + x^5 + x^2 + 1
x^10 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^1 + 1
x^10 + x^9 + x^4 + x^1 + 1
x^10 + x^9 + x^6 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^10 + x^9 + x^8 + x^6 + x^3 + x^2 + 1
x^10 + x^9 + x^8 + x^6 + x^5 + x^1 + 1
x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1
x^11 + x^2 + 1
x^11 + x^5 + x^3 + x^1 + 1
x^11 + x^5 + x^3 + x^2 + 1
x^11 + x^6 + x^5 + x^1 + 1
x^11 + x^7 + x^3 + x^2 + 1
x^11 + x^8 + x^5 + x^2 + 1
x^11 + x^8 + x^6 + x^5 + x^4 + x^1 + 1
x^11 + x^8 + x^6 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^11 + x^9 + x^4 + x^1 + 1
x^11 + x^9 + x^8 + x^7 + x^4 + x^1 + 1
x^11 + x^10 + x^3 + x^2 + 1
x^11 + x^10 + x^7 + x^4 + x^3 + x^1 + 1
x^11 + x^10 + x^8 + x^7 + x^5 + x^4 + x^3 + x^1 + 1
x^11 + x^10 + x^9 + x^8 + x^3 + x^1 + 1
x^12 + x^6 + x^4 + x^1 + 1
x^12 + x^9 + x^3 + x^2 + 1
x^12 + x^9 + x^8 + x^3 + x^2 + x^1 + 1
x^12 + x^10 + x^9 + x^8 + x^6 + x^2 + 1
x^12 + x^10 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1
x^12 + x^11 + x^6 + x^4 + x^2 + x^1 + 1
x^12 + x^11 + x^9 + x^5 + x^3 + x^1 + 1
x^12 + x^11 + x^9 + x^7 + x^6 + x^4 + 1
x^12 + x^11 + x^9 + x^7 + x^6 + x^5 + 1
x^12 + x^11 + x^9 + x^8 + x^7 + x^4 + 1
x^12 + x^11 + x^9 + x^8 + x^7 + x^5 + x^2 + x^1 + 1
x^12 + x^11 + x^10 + x^5 + x^2 + x^1 + 1
x^12 + x^11 + x^10 + x^8 + x^6 + x^4 + x^3 + x^1 + 1
x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^5 + x^4 + x^3 + x^1 + 1
x^13 + x^4 + x^3 + x^1 + 1
x^13 + x^9 + x^7 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^13 + x^9 + x^8 + x^7 + x^5 + x^1 + 1
x^13 + x^10 + x^9 + x^7 + x^5 + x^4 + 1
x^13 + x^10 + x^9 + x^8 + x^6 + x^3 + x^2 + x^1 + 1
x^13 + x^11 + x^8 + x^7 + x^4 + x^1 + 1
x^13 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^13 + x^12 + x^6 + x^5 + x^4 + x^3 + 1
x^13 + x^12 + x^8 + x^7 + x^6 + x^5 + 1
x^13 + x^12 + x^9 + x^8 + x^4 + x^2 + 1
x^13 + x^12 + x^10 + x^8 + x^6 + x^4 + x^3 + x^2 + 1
x^13 + x^12 + x^11 + x^5 + x^2 + x^1 + 1
x^13 + x^12 + x^11 + x^8 + x^7 + x^6 + x^4 + x^1 + 1
x^13 + x^12 + x^11 + x^9 + x^5 + x^3 + 1
x^14 + x^8 + x^6 + x^1 + 1
x^14 + x^10 + x^6 + x^1 + 1
x^14 + x^10 + x^9 + x^7 + x^6 + x^4 + x^3 + x^1 + 1
x^14 + x^11 + x^6 + x^1 + 1
x^14 + x^11 + x^9 + x^6 + x^5 + x^2 + 1
x^14 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + 1
x^14 + x^12 + x^11 + x^9 + x^8 + x^7 + x^6 + x^5 + x^3 + x^1 + 1
x^14 + x^12 + x^11 + x^10 + x^9 + x^7 + x^4 + x^3 + 1
x^14 + x^13 + x^6 + x^5 + x^3 + x^1 + 1
x^14 + x^13 + x^10 + x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^14 + x^13 + x^11 + x^6 + x^5 + x^4 + x^2 + x^1 + 1
x^14 + x^13 + x^11 + x^8 + x^5 + x^3 + x^2 + x^1 + 1
x^14 + x^13 + x^12 + x^11 + x^10 + x^7 + x^6 + x^1 + 1
x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^6 + x^5 + 1
x^15 + x^1 + 1
x^15 + x^4 + 1
x^15 + x^7 + 1
x^15 + x^7 + x^6 + x^3 + x^2 + x^1 + 1
x^15 + x^10 + x^5 + x^1 + 1
x^15 + x^10 + x^5 + x^4 + 1
x^15 + x^10 + x^5 + x^4 + x^2 + x^1 + 1
x^15 + x^10 + x^9 + x^7 + x^5 + x^3 + 1
x^15 + x^10 + x^9 + x^8 + x^5 + x^3 + 1
x^15 + x^11 + x^7 + x^6 + x^2 + x^1 + 1
x^15 + x^12 + x^3 + x^1 + 1
x^15 + x^12 + x^5 + x^4 + x^3 + x^2 + 1
x^15 + x^12 + x^11 + x^8 + x^7 + x^6 + x^4 + x^2 + 1
x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + 1
x^16 + x^9 + x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1
x^16 + x^12 + x^3 + x^1 + 1
x^16 + x^12 + x^7 + x^2 + 1
x^16 + x^13 + x^12 + x^10 + x^9 + x^7 + x^6 + x^1 + 1
x^16 + x^13 + x^12 + x^11 + x^7 + x^6 + x^3 + x^1 + 1
x^16 + x^13 + x^12 + x^11 + x^10 + x^6 + x^2 + x^1 + 1
x^16 + x^14 + x^10 + x^8 + x^3 + x^1 + 1
x^16 + x^14 + x^13 + x^12 + x^6 + x^5 + x^3 + x^2 + 1
x^16 + x^14 + x^13 + x^12 + x^10 + x^7 + 1
x^16 + x^15 + x^10 + x^6 + x^5 + x^3 + x^2 + x^1 + 1
x^16 + x^15 + x^11 + x^9 + x^8 + x^7 + x^5 + x^4 + x^2 + x^1 + 1
x^16 + x^15 + x^11 + x^10 + x^7 + x^6 + x^5 + x^3 + x^2 + x^1 + 1
x^16 + x^15 + x^11 + x^10 + x^9 + x^6 + x^2 + x^1 + 1
x^16 + x^15 + x^11 + x^10 + x^9 + x^8 + x^6 + x^4 + x^2 + x^1 + 1
x^17 + x^3 + 1
x^17 + x^3 + x^2 + x^1 + 1
x^17 + x^5 + 1
x^17 + x^6 + 1
x^17 + x^8 + x^4 + x^3 + 1
x^17 + x^8 + x^7 + x^6 + x^4 + x^3 + 1
x^17 + x^10 + x^9 + x^8 + x^6 + x^5 + x^3 + x^2 + 1
x^17 + x^12 + x^6 + x^3 + x^2 + x^1 + 1
x^17 + x^12 + x^9 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^17 + x^12 + x^9 + x^7 + x^6 + x^4 + x^3 + x^2 + 1
x^17 + x^14 + x^11 + x^7 + x^5 + x^3 + x^2 + x^1 + 1
x^17 + x^15 + x^13 + x^11 + x^9 + x^7 + x^5 + x^3 + 1
x^17 + x^15 + x^13 + x^11 + x^9 + x^7 + x^6 + x^4 + x^2 + x^1 + 1
x^17 + x^16 + x^3 + x^1 + 1
x^18 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^18 + x^7 + 1
x^18 + x^7 + x^5 + x^2 + x^1 + 1
x^18 + x^8 + x^2 + x^1 + 1
x^18 + x^9 + x^7 + x^6 + x^5 + x^4 + 1
x^18 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + x^1 + 1
x^18 + x^9 + x^8 + x^7 + x^6 + x^4 + x^2 + x^1 + 1
x^18 + x^10 + x^7 + x^5 + 1
x^18 + x^10 + x^8 + x^5 + 1
x^18 + x^10 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^18 + x^10 + x^9 + x^3 + 1
x^18 + x^13 + x^6 + x^4 + 1
x^18 + x^15 + x^5 + x^2 + 1
x^18 + x^15 + x^9 + x^2 + 1
x^19 + x^5 + x^2 + x^1 + 1
x^19 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^19 + x^6 + x^2 + x^1 + 1
x^19 + x^6 + x^5 + x^3 + x^2 + x^1 + 1
x^19 + x^6 + x^5 + x^4 + x^3 + x^2 + 1
x^19 + x^7 + x^5 + x^3 + x^2 + x^1 + 1
x^19 + x^8 + x^7 + x^5 + 1
x^19 + x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^19 + x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + x^1 + 1
x^19 + x^9 + x^8 + x^5 + 1
x^19 + x^9 + x^8 + x^6 + x^5 + x^3 + x^2 + x^1 + 1
x^19 + x^9 + x^8 + x^7 + x^4 + x^3 + x^2 + x^1 + 1
x^19 + x^11 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + 1
x^19 + x^11 + x^10 + x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + x^1 + 1
x^19 + x^16 + x^13 + x^10 + x^7 + x^4 + x^1 + 1
x^20 + x^3 + 1
x^20 + x^9 + x^5 + x^3 + 1
x^20 + x^11 + x^8 + x^6 + x^3 + x^2 + 1
x^20 + x^14 + x^10 + x^9 + x^8 + x^6 + x^5 + x^4 + 1
x^20 + x^17 + x^14 + x^10 + x^7 + x^4 + x^3 + x^2 + 1
x^20 + x^19 + x^4 + x^3 + 1
x^21 + x^2 + 1
x^21 + x^8 + x^7 + x^4 + x^3 + x^2 + 1
x^21 + x^10 + x^6 + x^4 + x^3 + x^2 + 1
x^21 + x^13 + x^5 + x^2 + 1
x^21 + x^14 + x^7 + x^2 + 1
x^21 + x^14 + x^7 + x^6 + x^3 + x^2 + 1
x^21 + x^14 + x^12 + x^7 + x^6 + x^4 + x^3 + x^2 + 1
x^21 + x^15 + x^10 + x^9 + x^5 + x^4 + x^3 + x^2 + 1
x^21 + x^20 + x^19 + x^18 + x^5 + x^4 + x^3 + x^2 + 1
x^22 + x^1 + 1
x^22 + x^9 + x^5 + x^1 + 1
x^22 + x^14 + x^13 + x^12 + x^7 + x^3 + x^2 + x^1 + 1
x^22 + x^17 + x^9 + x^7 + x^2 + x^1 + 1
x^22 + x^17 + x^13 + x^12 + x^8 + x^7 + x^2 + x^1 + 1
x^22 + x^20 + x^18 + x^16 + x^6 + x^4 + x^2 + x^1 + 1
x^23 + x^5 + 1
x^23 + x^5 + x^4 + x^1 + 1
x^23 + x^11 + x^10 + x^7 + x^6 + x^5 + 1
x^23 + x^12 + x^5 + x^4 + 1
x^23 + x^15 + x^10 + x^9 + x^7 + x^5 + x^4 + x^3 + 1
x^23 + x^16 + x^13 + x^6 + x^5 + x^3 + 1
x^23 + x^17 + x^11 + x^5 + 1
x^23 + x^17 + x^11 + x^9 + x^8 + x^5 + x^4 + x^1 + 1
x^23 + x^18 + x^16 + x^13 + x^11 + x^8 + x^5 + x^2 + 1
x^23 + x^21 + x^7 + x^5 + 1
x^24 + x^7 + x^2 + x^1 + 1
x^24 + x^21 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^10 + x^9 + x^5 + x^4 + x^1 + 1
x^24 + x^22 + x^20 + x^18 + x^16 + x^14 + x^11 + x^9 + x^8 + x^7 + x^5 + x^4 + 1
x^25 + x^3 + 1
x^25 + x^3 + x^2 + x^1 + 1
x^25 + x^11 + x^9 + x^8 + x^6 + x^4 + x^3 + x^2 + 1
x^25 + x^12 + x^4 + x^3 + 1
x^25 + x^12 + x^11 + x^8 + x^7 + x^6 + x^4 + x^3 + 1
x^25 + x^17 + x^10 + x^3 + x^2 + x^1 + 1
x^25 + x^18 + x^12 + x^11 + x^6 + x^5 + x^4 + x^3 + 1
x^25 + x^20 + x^5 + x^3 + 1
x^25 + x^20 + x^16 + x^11 + x^5 + x^3 + x^2 + x^1 + 1
x^25 + x^23 + x^21 + x^19 + x^9 + x^7 + x^5 + x^3 + 1
x^26 + x^6 + x^2 + x^1 + 1
x^26 + x^19 + x^16 + x^15 + x^14 + x^13 + x^11 + x^9 + x^8 + x^7 + x^6 + x^5 + x^3 + x^2 + 1
x^26 + x^21 + x^18 + x^16 + x^15 + x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^3 + 1
x^26 + x^22 + x^20 + x^19 + x^16 + x^13 + x^11 + x^9 + x^8 + x^7 + x^5 + x^4 + x^2 + x^1 + 1
x^26 + x^22 + x^21 + x^16 + x^12 + x^11 + x^10 + x^8 + x^5 + x^4 + x^3 + x^1 + 1
x^26 + x^23 + x^22 + x^21 + x^19 + x^18 + x^15 + x^14 + x^13 + x^11 + x^10 + x^9 + x^8 + x^6 + x^5 + x^2 + 1
x^26 + x^24 + x^21 + x^17 + x^16 + x^14 + x^13 + x^11 + x^7 + x^6 + x^4 + x^1 + 1
x^27 + x^5 + x^2 + x^1 + 1
x^27 + x^18 + x^11 + x^10 + x^9 + x^5 + x^4 + x^3 + 1
x^27 + x^22 + x^13 + x^11 + x^6 + x^5 + x^4 + x^3 + 1
x^27 + x^22 + x^17 + x^15 + x^14 + x^13 + x^6 + x^1 + 1
x^27 + x^22 + x^21 + x^20 + x^18 + x^17 + x^15 + x^13 + x^12 + x^7 + x^5 + 1
x^27 + x^24 + x^19 + x^16 + x^12 + x^8 + x^7 + x^3 + x^2 + x^1 + 1
x^27 + x^24 + x^21 + x^19 + x^16 + x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1
x^27 + x^25 + x^23 + x^21 + x^13 + x^11 + x^9 + x^8 + x^7 + x^6 + x^5 + x^3 + x^2 + x^1 + 1
x^27 + x^25 + x^23 + x^21 + x^20 + x^19 + x^18 + x^16 + x^14 + x^10 + x^8 + x^7 + x^4 + x^3 + 1
x^28 + x^3 + 1
x^28 + x^13 + x^11 + x^9 + x^5 + x^3 + 1
x^28 + x^18 + x^17 + x^16 + x^9 + x^5 + x^4 + x^3 + 1
x^28 + x^19 + x^17 + x^15 + x^10 + x^6 + x^3 + x^2 + 1
x^28 + x^22 + x^11 + x^10 + x^4 + x^3 + 1
x^28 + x^24 + x^20 + x^16 + x^12 + x^8 + x^4 + x^3 + 1
x^29 + x^2 + 1
x^29 + x^12 + x^7 + x^2 + 1
x^29 + x^18 + x^14 + x^6 + x^3 + x^2 + 1
x^29 + x^19 + x^16 + x^6 + x^3 + x^2 + 1
x^29 + x^20 + x^11 + x^2 + 1
x^29 + x^20 + x^16 + x^11 + x^8 + x^4 + x^3 + x^2 + 1
x^29 + x^21 + x^5 + x^2 + 1
x^29 + x^23 + x^10 + x^9 + x^5 + x^4 + x^3 + x^2 + 1
x^29 + x^24 + x^14 + x^13 + x^8 + x^4 + x^3 + x^2 + 1
x^29 + x^26 + x^5 + x^2 + 1
x^30 + x^23 + x^2 + x^1 + 1
x^30 + x^24 + x^20 + x^16 + x^14 + x^13 + x^11 + x^7 + x^2 + x^1 + 1
x^30 + x^24 + x^21 + x^20 + x^18 + x^15 + x^13 + x^12 + x^9 + x^7 + x^6 + x^4 + x^3 + x^1 + 1
x^30 + x^25 + x^24 + x^23 + x^19 + x^18 + x^16 + x^14 + x^11 + x^8 + x^6 + x^4 + x^3 + x^1 + 1
x^30 + x^27 + x^25 + x^24 + x^23 + x^22 + x^19 + x^16 + x^12 + x^10 + x^8 + x^7 + x^6 + x^1 + 1
x^31 + x^3 + 1
x^31 + x^3 + x^2 + x^1 + 1
x^31 + x^13 + x^8 + x^3 + 1
x^31 + x^16 + x^8 + x^4 + x^3 + x^2 + 1
x^31 + x^20 + x^15 + x^5 + x^4 + x^3 + 1
x^31 + x^20 + x^18 + x^7 + x^5 + x^3 + 1
x^31 + x^21 + x^12 + x^3 + x^2 + x^1 + 1
x^31 + x^23 + x^22 + x^15 + x^14 + x^7 + x^4 + x^3 + 1
x^31 + x^25 + x^19 + x^14 + x^7 + x^3 + x^2 + x^1 + 1
x^31 + x^27 + x^23 + x^19 + x^15 + x^11 + x^7 + x^3 + 1
x^31 + x^27 + x^23 + x^19 + x^15 + x^11 + x^10 + x^9 + x^7 + x^6 + x^5 + x^3 + x^2 + x^1 + 1
x^32 + x^22 + x^2 + x^1 + 1
x^32 + x^22 + x^21 + x^20 + x^18 + x^17 + x^15 + x^13 + x^12 + x^10 + x^8 + x^6 + x^4 + x^1 + 1
x^32 + x^23 + x^17 + x^16 + x^14 + x^10 + x^8 + x^7 + x^6 + x^5 + x^3 + 1
x^32 + x^26 + x^23 + x^22 + x^16 + x^12 + x^11 + x^10 + x^8 + x^7 + x^5 + x^4 + x^2 + x^1 + 1
x^32 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^17 + x^13 + x^11 + x^10 + x^9 + x^8 + x^7 + x^2 + x^1 + 1
x^32 + x^28 + x^19 + x^18 + x^16 + x^14 + x^11 + x^10 + x^9 + x^6 + x^5 + x^1 + 1