Zp2上灰度映射的多项式表示

Proceedings of 2011 IEEE International Conference on Intelligence and Security Informatics Pub Date : 2011-07-10 DOI:10.1109/ISI.2011.5984089

Lanlan Liu, Meng Zhou

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引用次数: 0

摘要

在本文中，我们用多项式表示法描述了在素数p2上的循环码，我们还讨论了Nechaev置换的多项式表示法以及Gray映射和Nechaev-Gray映射。然后通过Gray映射和Nechaev-Gray映射的多项式表示，将Gerardo Vega和Jacques Wolfman在[1]中关于l0 4的结果推广到l0 2。我们证明了在一个长度为n的线性码中，可以用多项式表示在一个长度为n的线性码中得到一个长度为pn的线性循环码。所以我们的结果是[1][3][4]中结果的推广，在[1][3][4]中他们只考虑了在4上的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The polynomial representation of Gray map on Zp2

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.

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Proceedings of 2011 IEEE International Conference on Intelligence and Security Informatics

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