On Self-dual and LCD Double Circulant Codes over a Non-chain Ring

YAO Ting; ZHU Shixin; KAI Xiaoshan

doi:10.1049/cje.2019.06.021

Volume 28 Issue 5

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YAO Ting, ZHU Shixin, KAI Xiaoshan, “On Self-dual and LCD Double Circulant Codes over a Non-chain Ring,” Chinese Journal of Electronics, vol. 28, no. 5, pp. 1018-1024, 2019, doi: 10.1049/cje.2019.06.021

Citation:

YAO Ting, ZHU Shixin, KAI Xiaoshan, “On Self-dual and LCD Double Circulant Codes over a Non-chain Ring,” Chinese Journal of Electronics, vol. 28, no. 5, pp. 1018-1024, 2019, doi: 10.1049/cje.2019.06.021

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On Self-dual and LCD Double Circulant Codes over a Non-chain Ring

doi: 10.1049/cje.2019.06.021

School of Mathematics, Hefei University of Technology, Hefei 230601, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61772168, No.61572168), the Natural Science Foundation of Anhui Province (No.1808085MA15), and Key University Science Research Project of Anhui Province (No.KJ2018A0497).

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Corresponding author: ZHU Shixin (corresponding author) was born in 1962.He is a professor and doctoral supervisor of Hefei University of Technology.His research interests include algebra code theory,information security and sequence cipher,etc.(Email:zhushixinmath@hfut.edu.cn)
Received Date: 2018-04-19
Rev Recd Date: 2018-07-28
Publish Date: 2019-09-10

Abstract

Abstract

In this paper, we study double circulant codes of length 2n over the non-chain ring R=F_q + vF_q + v²F _q, where q is an odd prime power and v³=v. Exact enumerations of self-dual and LCD double circulant codes of length 2n over R are derived. When n is an odd prime, using random coding, we obtain families of asymptotically good self-dual and LCD codes of length 6n over F_q.
- Double circulant codes,
- Non-chain ring,
- Self-dual codes,
- Linear complementary dual (LCD) codes,
- Artin conjecture

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References(17)

References

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