The weight hierarchies of three classes of linear codes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909213220929536 |
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| author | Lu, Wei Wang, Qingyao Wang, Xiaoqiang Zheng, Dabin |
| author_facet | Lu, Wei Wang, Qingyao Wang, Xiaoqiang Zheng, Dabin |
| contents | Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in various applications. However, determining the generalized Hamming weights of linear codes, particularly their weight hierarchy, is generally a challenging task. In this paper, we focus on investigating the generalized Hamming weights of three classes of linear codes over finite fields. These codes are constructed by different defining sets. By analysing the intersections between the definition sets and the duals of all $r$-dimensional subspaces, we get the inequalities on the sizes of these intersections. Then constructing subspaces that reach the upper bounds of these inequalities, we successfully determine the complete weight hierarchies of these codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The weight hierarchies of three classes of linear codes Lu, Wei Wang, Qingyao Wang, Xiaoqiang Zheng, Dabin Information Theory Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in various applications. However, determining the generalized Hamming weights of linear codes, particularly their weight hierarchy, is generally a challenging task. In this paper, we focus on investigating the generalized Hamming weights of three classes of linear codes over finite fields. These codes are constructed by different defining sets. By analysing the intersections between the definition sets and the duals of all $r$-dimensional subspaces, we get the inequalities on the sizes of these intersections. Then constructing subspaces that reach the upper bounds of these inequalities, we successfully determine the complete weight hierarchies of these codes. |
| title | The weight hierarchies of three classes of linear codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.19596 |