On Distances of Family of Constacyclic Codes over Finite Chain Rings

YUAN Jian; ZHU Shixin; KAI Xiaoshan

doi:10.11999/JEIT160392

Volume 39 Issue 3

Mar. 2017

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YUAN Jian, ZHU Shixin, KAI Xiaoshan. On Distances of Family of Constacyclic Codes over Finite Chain Rings[J]. Journal of Electronics & Information Technology, 2017, 39(3): 754-757. doi: 10.11999/JEIT160392

Citation:

YUAN Jian, ZHU Shixin, KAI Xiaoshan. On Distances of Family of Constacyclic Codes over Finite Chain Rings[J]. Journal of Electronics & Information Technology, 2017, 39(3): 754-757. doi: 10.11999/JEIT160392

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On Distances of Family of Constacyclic Codes over Finite Chain Rings

doi: 10.11999/JEIT160392

Funds:

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)

Received Date: 2016-04-22
Rev Recd Date: 2016-09-23
Publish Date: 2017-03-19

Abstract

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 andR* is the multiplicative group of units of R. In this paper, for any wR*, 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 overR 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.
- Constacyclic codes,
- Finite chain rings,
- Hamming distance,
- Homogeneous distance

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References(13)

References

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