Negacyclic codes over Galois rings of characteristic 2
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Authors: | ShiXin Zhu XiaoShan Kai |
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Institution: | 1. School of Mathematics, Hefei University of Technology, Hefei, 230009, China 2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, China
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Abstract: | We investigate negacyclic codes over the Galois ring GR(2 a ,m) of length N = 2 k n, where n is odd and k ? 0. We first determine the structure of u-constacyclic codes of length n over the finite chain ring $GR(2^a ,m)u]/\langle u^{2^k } + 1\rangle $ . Then using a ring isomorphism we obtain the structure of negacyclic codes over GR(2 a ,m) of length N = 2 k n (n odd) and explore the existence of self-dual negacyclic codes over GR(2 a ,m). A bound for the homogeneous distance of such negacyclic codes is also given. |
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Keywords: | negacyclic codes constacyclic codes Galois rings self-dual codes homogeneous distance |
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