Column Twisted Reed-Solomon Codes as MDS Codes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909008708763648 |
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| author | Liu, Wei Luo, Jinquan Wang, Puyin Zhai, Dengxin |
| author_facet | Liu, Wei Luo, Jinquan Wang, Puyin Zhai, Dengxin |
| contents | In this paper, we study column twisted Reed-Solomon(TRS) codes. We establish some sufficient conditions for these codes to be MDS and show that the dimension of their Schur square codes is $2k$. Consequently, these TRS codes are shown to be not equivalent to Reed-Solomon(RS) codes. Moreover, our construction offers more flexible parameters than existing twisted generalized Reed-Solomon(TGRS) code designs. For a large odd prime power $q$, systematically constructed TGRS codes are known to be limited to length $\frac{q+1}{2}$. By contrast, our column TRS construction supports code lengths up to $\frac{q+3}{2}$. Finally, we present the dual codes of column TRS codes. Overall, this work introduces a new method for constructing MDS codes by appending column vectors to some generator matrix of an RS code. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_08755 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Column Twisted Reed-Solomon Codes as MDS Codes Liu, Wei Luo, Jinquan Wang, Puyin Zhai, Dengxin Information Theory In this paper, we study column twisted Reed-Solomon(TRS) codes. We establish some sufficient conditions for these codes to be MDS and show that the dimension of their Schur square codes is $2k$. Consequently, these TRS codes are shown to be not equivalent to Reed-Solomon(RS) codes. Moreover, our construction offers more flexible parameters than existing twisted generalized Reed-Solomon(TGRS) code designs. For a large odd prime power $q$, systematically constructed TGRS codes are known to be limited to length $\frac{q+1}{2}$. By contrast, our column TRS construction supports code lengths up to $\frac{q+3}{2}$. Finally, we present the dual codes of column TRS codes. Overall, this work introduces a new method for constructing MDS codes by appending column vectors to some generator matrix of an RS code. |
| title | Column Twisted Reed-Solomon Codes as MDS Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2507.08755 |