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The polynomial representation of Gray map on Zp2

In this work we describe cyclic code on ℤ<inf>p2</inf> 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 [1] on ℤ<inf>4</inf> to ℤ<inf>p2</inf> by polynomial representation of Gray and Nechaev-Gray maps. We proved that from a linear code ℤ<inf>p2</inf> of length n a linear cyclic code on ℤ<inf>p</inf> of length pn can be obtained using the polynomial representation of Gray and Nechaev-Gray maps on ℤ<inf>p</inf>. So our results are a generalization of the results in [1],[3],[4] where they only thought about the case of on ℤ<inf>4</inf>.