Some MDS codes over dihedral groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909506655485952 |
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| author | Wang, Yuchao |
| author_facet | Wang, Yuchao |
| contents | In this paper,we show some $[2n,2n-2,3]$ and $[2n,2n-3,4]$ MDS codes over dihedral codes $F_qD_{2n}$,in the case $n$ is odd and char$F_q$$\nmid$$\lvert G \rvert$ and $F_q$ contains primitive root of exponent $\lvert G \rvert$ i.e $F_q$ is the splitting field of $G$.Before that,we will give the Wedderburn decomposition and specific forms of linear primitive idempotents of $F_qD_{2n}$ under the above conditions.The MDS codes we construct are obtained by its Wedderburn decomposition and linear primitive idempotents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some MDS codes over dihedral groups Wang, Yuchao Information Theory In this paper,we show some $[2n,2n-2,3]$ and $[2n,2n-3,4]$ MDS codes over dihedral codes $F_qD_{2n}$,in the case $n$ is odd and char$F_q$$\nmid$$\lvert G \rvert$ and $F_q$ contains primitive root of exponent $\lvert G \rvert$ i.e $F_q$ is the splitting field of $G$.Before that,we will give the Wedderburn decomposition and specific forms of linear primitive idempotents of $F_qD_{2n}$ under the above conditions.The MDS codes we construct are obtained by its Wedderburn decomposition and linear primitive idempotents. |
| title | Some MDS codes over dihedral groups |
| topic | Information Theory |
| url | https://arxiv.org/abs/2502.16590 |