The Weight Distribution of a Class of <i>p</i>-Ary Cyclic Codes with Few Weights

LIU Li; XIE Xianhong

doi:10.1049/cje.2020.05.018

Volume 29 Issue 4

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LIU Li and XIE Xianhong, “The Weight Distribution of a Class of p-Ary Cyclic Codes with Few Weights,” Chinese Journal of Electronics, vol. 29, no. 4, pp. 717-723, 2020, doi: 10.1049/cje.2020.05.018

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LIU Li and XIE Xianhong, “The Weight Distribution of a Class of p-Ary Cyclic Codes with Few Weights,” Chinese Journal of Electronics, vol. 29, no. 4, pp. 717-723, 2020, doi: 10.1049/cje.2020.05.018

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The Weight Distribution of a Class of p-Ary Cyclic Codes with Few Weights

doi: 10.1049/cje.2020.05.018

LIU Li¹,
XIE Xianhong^2
,

1.
School of Mathematics, Hefei University of Technology, Hefei 230009, China;
2.
Key Laboratory of Electromagnetic Space Information, CAS, University of Science and Technology of China, Hefei 230027, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61572168, No.11871187) and the Anhui Provincial Natural Science Foundation (No.1508085SQA198).

Received Date: 2019-07-31
Rev Recd Date: 2019-11-13
Publish Date: 2020-07-10

Abstract

Abstract

In this paper, we investigate a class of p-ary cyclic codes whose duals have two zeros for some special cases and calculate their weight distributions explicitly. The results show that the codes have at most five nonzero weights. Moreover, they contain some optimal threeweight codes meeting the Griesmer bound.
- Cyclic codes,
- Weight distributions,
- Fourier expansion,
- Gauss sums,
- Griesmer bound

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References(25)

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