# Revision history [back]

### construction of extension field over GF(2^3)

My base field is GF(2^3) and to construct the field i am using irreducible polynomial p(x)=x^3+x+1. the extension field is GF(2^3)^2 and i want to construct this field using irreducible polynomial p(z)= z^2+(a^2+a+1)*z+a^2 where (a^2+a+1 and a^2 are the elements of field GF(2^3)) where a is represent theta that is root of irreducible polynomial over GF(2^3) . i have written the code in sage but it gives me error .

 2 None tmonteil 25328 ●29 ●180 ●472 http://wiki.sagemath.o...

### construction of extension field over GF(2^3)

My base field is GF(2^3) and to construct the field i am using irreducible polynomial p(x)=x^3+x+1. the extension field is GF(2^3)^2 and i want to construct this field using irreducible polynomial p(z)= z^2+(a^2+a+1)*z+a^2 where (a^2+a+1 and a^2 are the elements of field GF(2^3)) where a is represent theta that is root of irreducible polynomial over GF(2^3) . i have written the code in sage but it gives me error .

K.<a>=GF(2^3);K.modulus()
for i in enumerate(K):  print i
K1. K1.<b> = GF(K,'modulus=x^2+(a^2+a+1)*x+a^2');K1.modulus()      GF(K,'modulus=x^2+(a^2+a+1)*x+a^2');K1.modulus()