Three Classes of Optimal Ternary Cyclic Codes and the Weight Distributions of Their Duals

LI Lanqiang; ZHU Shixin; LIU Li

doi:10.1049/cje.2019.04.001

Volume 28 Issue 4

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LI Lanqiang, ZHU Shixin, LIU Li, “Three Classes of Optimal Ternary Cyclic Codes and the Weight Distributions of Their Duals,” Chinese Journal of Electronics, vol. 28, no. 4, pp. 674-681, 2019, doi: 10.1049/cje.2019.04.001

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LI Lanqiang, ZHU Shixin, LIU Li, “Three Classes of Optimal Ternary Cyclic Codes and the Weight Distributions of Their Duals,” Chinese Journal of Electronics, vol. 28, no. 4, pp. 674-681, 2019, doi: 10.1049/cje.2019.04.001

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Three Classes of Optimal Ternary Cyclic Codes and the Weight Distributions of Their Duals

doi: 10.1049/cje.2019.04.001

School of Mathematics, Hefei University of Technology, Hefei 230009, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61772168, No.11871187), the Natural Science Foundation of Anhui Province (No.1808085MA15), and the 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 received the Ph.D. degree in computer and information from Hefei University of Technology, Hefei, China, in 2005. Currently, he is a professor with the School of Mathematics, Hefei University of Technology. His research interests include information theory, coding theory, cryptography, and sequences. (Email:zhushixinmath@hfut.edu.cn)
Received Date: 2018-09-07
Rev Recd Date: 2019-03-19
Publish Date: 2019-07-10

Abstract

Abstract

Cyclic codes as a subclass of linear codes have wide applications in communication systems, consumer electronics and data storage systems, due to their efficient encoding and decoding algorithms. We construct three classes of optimal ternary cyclic codes, which meet some certain bound. The weight distributions of their duals are also completely determined. The results show that their duals have few nonzero weights.
- Finite field,
- Cyclic code,
- Optimal code,
- Duals,
- Weight distribution

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