Cardinality-consistent flag codes with longer type vectors
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908761392676864 |
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| author | Jia, Junfeng Chang, Yanxun |
| author_facet | Jia, Junfeng Chang, Yanxun |
| contents | Flag codes generalize constant dimension codes by considering sequences of nested subspaces with prescribed dimensions as codewords. A comprehensive construction, which unites cyclic orbit flag codes, yields two families of flag codes on $\mathbb{F}^n_q$ (where $n=sk+h$ with $s\geq 2$ and $0\leq h < k$): optimum distance flag codes of the longest possible type vector $(1, 2, \ldots, k, n-k, \ldots, n-1)$ and flag codes with longer type vectors $(1, 2, \ldots, k+h, 2k+h, \ldots, (s-2)k+h, n-k, \ldots, n-1)$. These flag codes achieve the same cardinality $\sum^{s-1}_{i=1}q^{ik+h}+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08144 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cardinality-consistent flag codes with longer type vectors Jia, Junfeng Chang, Yanxun Information Theory Combinatorics 11T71, 05E18 Flag codes generalize constant dimension codes by considering sequences of nested subspaces with prescribed dimensions as codewords. A comprehensive construction, which unites cyclic orbit flag codes, yields two families of flag codes on $\mathbb{F}^n_q$ (where $n=sk+h$ with $s\geq 2$ and $0\leq h < k$): optimum distance flag codes of the longest possible type vector $(1, 2, \ldots, k, n-k, \ldots, n-1)$ and flag codes with longer type vectors $(1, 2, \ldots, k+h, 2k+h, \ldots, (s-2)k+h, n-k, \ldots, n-1)$. These flag codes achieve the same cardinality $\sum^{s-1}_{i=1}q^{ik+h}+1$. |
| title | Cardinality-consistent flag codes with longer type vectors |
| topic | Information Theory Combinatorics 11T71, 05E18 |
| url | https://arxiv.org/abs/2601.08144 |