Description

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

Downloads

primitive_polynomials_GF2.txt
primitive_polynomials_GF2_extended.zip

Degree 2

 x^2 + x^1 + 1 

Degree 3

 x^3 + x^1 + 1 

Degree 4

 x^4 + x^1 + 1 

Degree 5

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

Degree 6

 x^6 + x^1 + 1 x^6 + x^5 + x^2 + x^1 + 1 x^6 + x^5 + x^3 + x^2 + 1 

Degree 7

 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 

Degree 8

 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 

Degree 9

 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 

Degree 10

 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 

Degree 11

 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 

Degree 12

 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 

Degree 13

 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 

Degree 14

 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 

Degree 15

 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 

Degree 16

 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 

Degree 17

 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 

Degree 18

 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 

Degree 19

 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 

Degree 20

 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 

Degree 21

 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 

Degree 22

 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 

Degree 23

 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 

Degree 24

 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 

Degree 25

 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 

Degree 26

 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 

Degree 27

 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 

Degree 28

 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 

Degree 29

 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 

Degree 30

 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 

Degree 31

 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 

Degree 32

 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 

Credits

• Coherent Spread Spectrum Systems - J.K. Holmes
• Digital Communications And Spread Spectrum Systems - Rodger E. Ziemer and Roger L. Peterson
• Error Control Coding - S. Lin, D. Costello
• Error Correction Codes - W.W. Peterson And E.J. Weldon
• On Primitive Trinomials - N. Zierler and J. Brillhart
• Primitive Polynomials (Mod 2) - By E.J. Watson
• Sequence A011260/M0107 - N. J. A. Sloane
• Tables of Irreducible Polynomials For The First Four Prime Moduli - R. Church
• Primitive Polynomial Generation Algorithms Implementation And Performance Analysis