The polynomial representation of Gray map on Zp2

Abstract

In this work we describe cyclic code on ℤp2 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 ℤ4 to ℤp2 by polynomial representation of Gray and Nechaev-Gray maps. We proved that from a linear code ℤp2 of length n a linear cyclic code on ℤp of length pn can be obtained using the polynomial representation of Gray and Nechaev-Gray maps on ℤp. So our results are a generalization of the results in [1],[3],[4] where they only thought about the case of on ℤ4.