New Constructions of Full Flag Codes Based on Partial Spreads
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916798899683328 |
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| author | Han, Xiang Li, Xinran Wang, Gang |
| author_facet | Han, Xiang Li, Xinran Wang, Gang |
| contents | Flag codes are a class of multishot network codes comprising sequences of nested subspaces (flags) within the vector space $\mathbb{F}_q^n$, where $q$ is a prime power. In this paper, we propose a family of constructions for full flag codes based on partial spreads. The distances of this family include maximum distance (optimum distance flag codes), second-maximum distance (quasi-optimum distance flag codes), as well as other feasible values. The structure of these flag codes resembles that of a \textquotedblleft sandwich", consisting of one layer of companion matrix and two layers of partial spreads. Furthermore, we present an efficient decoding algorithm for these codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New Constructions of Full Flag Codes Based on Partial Spreads Han, Xiang Li, Xinran Wang, Gang Information Theory Flag codes are a class of multishot network codes comprising sequences of nested subspaces (flags) within the vector space $\mathbb{F}_q^n$, where $q$ is a prime power. In this paper, we propose a family of constructions for full flag codes based on partial spreads. The distances of this family include maximum distance (optimum distance flag codes), second-maximum distance (quasi-optimum distance flag codes), as well as other feasible values. The structure of these flag codes resembles that of a \textquotedblleft sandwich", consisting of one layer of companion matrix and two layers of partial spreads. Furthermore, we present an efficient decoding algorithm for these codes. |
| title | New Constructions of Full Flag Codes Based on Partial Spreads |
| topic | Information Theory |
| url | https://arxiv.org/abs/2506.15127 |