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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.02262 |
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| _version_ | 1866913179952480256 |
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| author | Wang, Xiaoqiang Song, Xun Zheng, Dabin Chen, Hao Ding, Cunsheng |
| author_facet | Wang, Xiaoqiang Song, Xun Zheng, Dabin Chen, Hao Ding, Cunsheng |
| contents | In spite of the intensive study of cyclic codes and the recent construction of an infinite family of self-dual binary cyclic codes whose minimum distances have the square-root bound in IEEE Trans. IT, vol. 71, no. 4, 2025, it is still a 70-year-old open problem whether there is an infinite family of self-dual binary cyclic codes whose minimum distances have a lower bound better than the square-root bound. This paper settles this long-standing open problem in coding theory by presenting infinite families of such self-dual binary cyclic codes. As by-products, several families of cyclic codes with better parameters than those in some references are also constructed in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02262 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound Wang, Xiaoqiang Song, Xun Zheng, Dabin Chen, Hao Ding, Cunsheng Information Theory 94B15 In spite of the intensive study of cyclic codes and the recent construction of an infinite family of self-dual binary cyclic codes whose minimum distances have the square-root bound in IEEE Trans. IT, vol. 71, no. 4, 2025, it is still a 70-year-old open problem whether there is an infinite family of self-dual binary cyclic codes whose minimum distances have a lower bound better than the square-root bound. This paper settles this long-standing open problem in coding theory by presenting infinite families of such self-dual binary cyclic codes. As by-products, several families of cyclic codes with better parameters than those in some references are also constructed in this paper. |
| title | Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound |
| topic | Information Theory 94B15 |
| url | https://arxiv.org/abs/2606.02262 |