Primitive polynomial in GF(4) ?

[mahesh_2961]

primitive polynomial in GF(4) ??

Hai All,
I m required to make a pseudo random generator. I know that i can make that using some Flip flops and XOR gates(in linear feedback shift register configuration ). But the resulting PN sequences will be in Galois Field(2) as the taps for the flip flops are according to the coefficients of a primitive polynomial in GF(2).

So i was just thinking if there is any primitive polynomial in GF(4)? I need to make a pn sequence of length 1023. In GF(2), the tap weights for the linear feedback shift register is the coefficient of primitive polynomial of order 10 . So in GF(4), if a primitive polynomial exists, a primitive polynomial of order 5 will give taps for an LFSR to generate PNsequence of length 1023 .
Is there a primitive polynomial of order >5 in GF(4) ?

i searched the net but couldn't get any information regarding this ..

thanks in advance
Mahesh

 

[fresh_42]

E.g. take the $n$-th root of unity, where $n$ is odd and consider its irreducible polynomial over $GF(4)$.