Symplectic self-orthogonal quasi-cyclic codes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913883292172288 |
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| author | Guan, Chaofeng Li, Ruihu Lv, Jingjie Ma, Zhi |
| author_facet | Guan, Chaofeng Li, Ruihu Lv, Jingjie Ma, Zhi |
| contents | In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of $1$-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct numerous new binary symplectic self-orthogonal QC codes with excellent parameters, leading to $117$ record-breaking quantum error-correction codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14225 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Symplectic self-orthogonal quasi-cyclic codes Guan, Chaofeng Li, Ruihu Lv, Jingjie Ma, Zhi Information Theory In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of $1$-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct numerous new binary symplectic self-orthogonal QC codes with excellent parameters, leading to $117$ record-breaking quantum error-correction codes. |
| title | Symplectic self-orthogonal quasi-cyclic codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2212.14225 |