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| On Distances of Family of Constacyclic Codes over Finite Chain Rings |
| YUAN Jian ZHU Shixin KAI Xiaoshan |
(School of Mathematics, Hefei University of Technology, Hefei 230009, China)
(National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China) |
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Abstract In coding theory, the (minimum) distance of a code is a very important invariant, which always determines the error-correcting capability of the code. Let R be an arbitrary commutative finite chain ring, a is a generator of the unique maximal ideal and R* is the multiplicative group of units of R. In this paper, for any w∈R*, by using the generator polynomials of (1+aw)-constacyclic codes of any length over R, higher torsion codes of such codes are calculated. The Hamming distance of all (1+aw)-constacyclic codes of any length over R is determined and the exact homogeneous distance of some such codes is obtained. The result provides a theoretical basis for encoding and decoding for such constacyclic codes.
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Received: 22 April 2016
Published: 14 November 2016
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| Fund: The National Natural Science Foundation of China (61370089, 60973125), The Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (2014D04), The Natural Science Foundation of Anhui Province (1508085SQA198) |
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Corresponding Authors:
ZHU Shixin
E-mail: zhushixin@hfut.edu.cn
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