The polynomial representation of Gray map on Zp2

In this work we describe cyclic code on ℤ_p2 by polynomial representation, we also discuss polynomial representation of Nechaev permutation and the Gray and Nechaev-Gray maps. Then we extend Gerardo Vega and Jacques Wolfman´s result in on ℤ₄ to ℤ_p2 by polynomial representation of Gray and Nechaev-Gray maps. We proved that from a linear code ℤ_p2 of length n a linear cyclic code on ℤ_p of length pn can be obtained using the polynomial representation of Gray and Nechaev-Gray maps on ℤ_p. So our results are a generalization of the results in where they only thought about the case of on ℤ₄.