On the weights of linear codes with prescribed automorphisms
The number of nonzero weights of a linear code is essential in coding theory as it unveils salient properties of the code, such as its covering radius. In this paper, we establish two upper bounds on the number of nonzero weights of a linear code with prescribed automorphism. Our bounds are applicab...
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sg-ntu-dr.10356-1749982024-04-22T15:36:54Z On the weights of linear codes with prescribed automorphisms Luo, Gaojun Cao, Xiwang Ezerman, Martianus Frederic Ling, San School of Physical and Mathematical Sciences Division of Mathematical Sciences Nanjing University of Aeronautics and Astronautics Mathematical Sciences Automorphism Covering radius Hamming weight Linear code Upper bound The number of nonzero weights of a linear code is essential in coding theory as it unveils salient properties of the code, such as its covering radius. In this paper, we establish two upper bounds on the number of nonzero weights of a linear code with prescribed automorphism. Our bounds are applicable for almost all linear codes and tighter than previously known bounds. Examples confirm that our bounds are sharp on numerous occasions. In addition, we give an infinite family of linear codes that attain our bounds with equality. Nanyang Technological University Submitted/Accepted version G. Luo, M. F. Ezerman, and S. Ling are supported by Nanyang Technological University Research Grant No. 04INS000047C230GRT01. X. Cao and G. Luo are supported by the National Natural Science Foundation of China Grant No. 12171241 and No. 12226408 and Natural Science Foundation of Jiangsu Province Grant No. BK20230867. 2024-04-18T07:37:48Z 2024-04-18T07:37:48Z 2023 Journal Article Luo, G., Cao, X., Ezerman, M. F. & Ling, S. (2023). On the weights of linear codes with prescribed automorphisms. IEEE Transactions On Information Theory. https://dx.doi.org/10.1109/TIT.2023.3347701 0018-9448 https://hdl.handle.net/10356/174998 10.1109/TIT.2023.3347701 en 04INS000047C230GRT01 IEEE Transactions on Information Theory © 2023 IEEE. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1109/TIT.2023.3347701. application/pdf |
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Mathematical Sciences Automorphism Covering radius Hamming weight Linear code Upper bound |
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Mathematical Sciences Automorphism Covering radius Hamming weight Linear code Upper bound Luo, Gaojun Cao, Xiwang Ezerman, Martianus Frederic Ling, San On the weights of linear codes with prescribed automorphisms |
| description |
The number of nonzero weights of a linear code is essential in coding theory as it unveils salient properties of the code, such as its covering radius. In this paper, we establish two upper bounds on the number of nonzero weights of a linear code with prescribed automorphism. Our bounds are applicable for almost all linear codes and tighter than previously known bounds. Examples confirm that our bounds are sharp on numerous occasions. In addition, we give an infinite family of linear codes that attain our bounds with equality. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Luo, Gaojun Cao, Xiwang Ezerman, Martianus Frederic Ling, San |
| format |
Article |
| author |
Luo, Gaojun Cao, Xiwang Ezerman, Martianus Frederic Ling, San |
| author_sort |
Luo, Gaojun |
| title |
On the weights of linear codes with prescribed automorphisms |
| title_short |
On the weights of linear codes with prescribed automorphisms |
| title_full |
On the weights of linear codes with prescribed automorphisms |
| title_fullStr |
On the weights of linear codes with prescribed automorphisms |
| title_full_unstemmed |
On the weights of linear codes with prescribed automorphisms |
| title_sort |
on the weights of linear codes with prescribed automorphisms |
| publishDate |
2024 |
| url |
https://hdl.handle.net/10356/174998 |
| _version_ |
1814047394284699648 |