Several classes of three-weight or four-weight linear codes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912685127368704 |
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| author | Liao, Qunying Zhang, Zhaohui Zheng, Peipei |
| author_facet | Liao, Qunying Zhang, Zhaohui Zheng, Peipei |
| contents | In this manuscript, we construct a class of projective three-weight linear codes and two classes of projective four-weight linear codes over F2 from the defining sets construction, and determine their weight distributions by using additive characters. Especially, the projective three-weight linear code and one class of projective four-weight linear codes (Theorem 4.1) can be applied in secret sharing schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Several classes of three-weight or four-weight linear codes Liao, Qunying Zhang, Zhaohui Zheng, Peipei Information Theory 11T71 E.4 In this manuscript, we construct a class of projective three-weight linear codes and two classes of projective four-weight linear codes over F2 from the defining sets construction, and determine their weight distributions by using additive characters. Especially, the projective three-weight linear code and one class of projective four-weight linear codes (Theorem 4.1) can be applied in secret sharing schemes. |
| title | Several classes of three-weight or four-weight linear codes |
| topic | Information Theory 11T71 E.4 |
| url | https://arxiv.org/abs/2511.01309 |