Abstract
In this work we describe cyclic code on ℤ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> to ℤ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p2</inf> by polynomial representation of Gray and Nechaev-Gray maps. We proved that from a linear code ℤ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p2</inf> of length n a linear cyclic code on ℤ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> of length pn can be obtained using the polynomial representation of Gray and Nechaev-Gray maps on ℤ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> .
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