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Two classes of linear codes and their weight distributions

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Abstract

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, two classes of linear codes over the finite field \({\mathrm {GF}}(p)\) are presented and their weight distributions are also determined, where p is an odd prime. Some of the linear codes obtained are optimal or almost optimal in the sense that their parameters meet certain bound on linear codes.

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Acknowledgements

The authors are very grateful to the three reviewers for their comments and suggestions that improved the presentation and quality of this paper. The research of C. Xiang was supported by the National Natural Science Foundation of China (No. 11701187) and the PhD Start-up Fund of the Natural Science Foundation of Guangdong Province of China (No. 2017A030310522). The research of X. Wang and F. Fu was supported by the National Key Basic Research Program of China (Grant No. 2013CB834204), and the National Natural Science Foundation of China (Grant Nos. 61571243 and 61171082). The research of C. Tang was supported by NSFC No. 11401480, 11531002. C. Tang also acknowledges support from 14E013 and CXTD2014-4 of China West Normal University.

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Correspondence to Xianfang Wang.

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Xiang, C., Wang, X., Tang, C. et al. Two classes of linear codes and their weight distributions. AAECC 29, 209–225 (2018). https://doi.org/10.1007/s00200-017-0338-7

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