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The weight distributions of some cyclic codes with three or four nonzeros over \(\mathbb F _3\)

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Abstract

Because of efficient encoding and decoding algorithms comparing with linear block codes, cyclic codes form an important family and have applications in communications and storage systems. However, their weight distributions are known only for a few cases mainly on the codes with no more than three nonzeros. In this paper, the weight distributions of two classes of cyclic codes with three or four nonzeros are determined.

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Acknowledgments

This work is supported in part by the National Key Basic Research and Development Plan of China under Grant 2012CB316100, and the National Natural Science Foundation of China under Grants 61271222, 60972033. We would also like to acknowledge the foundation TS0520103001 of Shanghai Jiao Tong University and University of Leuven.

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  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Min Hang District, Shanghai, 200240, China

    Xiaogang Liu & Yuan Luo

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  1. Xiaogang Liu
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  2. Yuan Luo
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Correspondence to Yuan Luo.

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Communicated by S. Ball.

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Liu, X., Luo, Y. The weight distributions of some cyclic codes with three or four nonzeros over \(\mathbb F _3\) . Des. Codes Cryptogr. 73, 747–768 (2014). https://doi.org/10.1007/s10623-013-9824-5

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  • DOI: https://doi.org/10.1007/s10623-013-9824-5

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