Three new constructions of optimal linear codes with few weights
Linear codes play a key role in widespread applications. In this paper, we propose three new constructions of linear codes. We give some sufficient conditions for the constructed linear codes to be optimal or distance-optimal in terms of the Griesmer bound. Three classes of distance-optimal linear c...
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sg-ntu-dr.10356-1734942024-02-07T04:28:44Z Three new constructions of optimal linear codes with few weights Cheng, Yingjie Cao, Xiwang Luo, Gaojun School of Physical and Mathematical Sciences Mathematical Sciences Linear Code Griesmer Code Linear codes play a key role in widespread applications. In this paper, we propose three new constructions of linear codes. We give some sufficient conditions for the constructed linear codes to be optimal or distance-optimal in terms of the Griesmer bound. Three classes of distance-optimal linear codes with new parameters are presented. Under some constraints, we show that some of the presented linear codes have few weights. This research is supported by the National Natural Science Foundation of China under Grant 12171241 and Grant 62172183, China Scholarship Counsil Scholarship Program under Grant 202206830084 and Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant KYCX22_0324. 2024-02-07T04:28:44Z 2024-02-07T04:28:44Z 2023 Journal Article Cheng, Y., Cao, X. & Luo, G. (2023). Three new constructions of optimal linear codes with few weights. Computational and Applied Mathematics, 42(7), 321-. https://dx.doi.org/10.1007/s40314-023-02472-x 0101-8205 https://hdl.handle.net/10356/173494 10.1007/s40314-023-02472-x 2-s2.0-85173626403 7 42 321 en Computational and Applied Mathematics © 2023 The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional. All rights reserved. |
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Mathematical Sciences Linear Code Griesmer Code |
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Mathematical Sciences Linear Code Griesmer Code Cheng, Yingjie Cao, Xiwang Luo, Gaojun Three new constructions of optimal linear codes with few weights |
| description |
Linear codes play a key role in widespread applications. In this paper, we propose three new constructions of linear codes. We give some sufficient conditions for the constructed linear codes to be optimal or distance-optimal in terms of the Griesmer bound. Three classes of distance-optimal linear codes with new parameters are presented. Under some constraints, we show that some of the presented linear codes have few weights. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Cheng, Yingjie Cao, Xiwang Luo, Gaojun |
| format |
Article |
| author |
Cheng, Yingjie Cao, Xiwang Luo, Gaojun |
| author_sort |
Cheng, Yingjie |
| title |
Three new constructions of optimal linear codes with few weights |
| title_short |
Three new constructions of optimal linear codes with few weights |
| title_full |
Three new constructions of optimal linear codes with few weights |
| title_fullStr |
Three new constructions of optimal linear codes with few weights |
| title_full_unstemmed |
Three new constructions of optimal linear codes with few weights |
| title_sort |
three new constructions of optimal linear codes with few weights |
| publishDate |
2024 |
| url |
https://hdl.handle.net/10356/173494 |
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1794549345985495040 |