Construction of a Class of Linear Codes with Four-weight and Six-weight

Xiaoni DU; Hongxia LÜ; Rong WANG

doi:10.11999/JEIT180939

Volume 41 Issue 12

Dec. 2019

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Xiaoni DU, Hongxia LÜ, Rong WANG. Construction of a Class of Linear Codes with Four-weight and Six-weight[J]. Journal of Electronics & Information Technology, 2019, 41(12): 2995-2999. doi: 10.11999/JEIT180939

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Xiaoni DU, Hongxia LÜ, Rong WANG. Construction of a Class of Linear Codes with Four-weight and Six-weight[J]. Journal of Electronics & Information Technology, 2019, 41(12): 2995-2999. doi: 10.11999/JEIT180939

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Construction of a Class of Linear Codes with Four-weight and Six-weight

doi: 10.11999/JEIT180939

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Funds: The National Natural Science Foundtion of China (61772022, 61562077), The Shanghai Natural Science Foundation (16ZR1411200)

Received Date: 2018-10-09
Rev Recd Date: 2019-03-18

Available Online: 2019-04-25

Publish Date: 2019-12-01

Abstract

Abstract

Due to the wide applications in association schemes, authentication codes and secret sharing schemes etc., construction of the linear codes with a few weights is an important research topic. A class of linear codes with four-weight and six-weight over finite field ${F_p}$ (p is an odd prime) is constructed by a proper selection of the defining set. The explicit weight distribution is obtained using Gauss sums, and some examples from Magma program to illustrate the validity of the conclusions are provided. The results show that these codes include almost optimal codes with respect to Singleton bound.
- Linear codes,
- Authentication codes,
- Weight distribution,
- Gauss sums

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References(16)

References

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