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Please advise if somebody knows:

The polynomial x^2+x+2 ∈ F3^2is irreducible and i am looking for the generator polynomial, the length and dimension.

What i did its: Find the vector-exponent equivalence for each element 0-> (0,0) a->(0,1) a^2->(1,2) a^3->(2,2) a^4->(2,0) a^5->(0,2) a^6->(2,1) a^7->(1,1) a^8->(1,0)

the generator g(x) can be obtained assuming that a, a^2,a^3 are within its roots, so the g(x)=(x-a)(x-a^2)(x-a^3). And when i multiply (x-a)(x-a^2)(x-a^3), i get few elements but i am not sure if the generator polynomial is the result or i need to do something more.

thanks

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    polynomial in **F**3^2? What does it mean? – 2017-01-14
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    Do you mean $x^2+x+2\in \mathbb F_{3^2}[x]$? Also, what's a "generator polynomial"? – 2017-01-14
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    yes, i mean that. There is one and only one nonzero code polynomial (or code vector) of minimum degree (n-k) in a (n, k) cyclic code. This polynomial is called generator polynomial and is of the form g(x) = 1 + g1x + g2x^2 + + gn-k-1x^n-k-1 + x^n-k – 2017-01-15

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