Row-Column Twisted Reed-Solomon codes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909776343990272 |
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| author | Bhagat, Anuj Kumar Singh, Harshdeep Sarma, Ritumoni |
| author_facet | Bhagat, Anuj Kumar Singh, Harshdeep Sarma, Ritumoni |
| contents | In this article, we present a new class of codes known as row-column twisted Reed-Solomon codes (abbreviated as RCTRS), motivated by the works of \cite{beelen2017twisted} and \cite{liu2025column}. We explicitly provide conditions for such codes to be MDS and also ensure their existence. By determining the dimensions of their Schur squares, we prove that these MDS codes are not equivalent to Reed-Solomon codes, thus presenting a new family of non-RS MDS codes. Additionally, we prove that these MDS codes are also not equivalent to column twisted Reed-Solomon codes described in \cite{liu2025column}, showing the novelty of our construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Row-Column Twisted Reed-Solomon codes Bhagat, Anuj Kumar Singh, Harshdeep Sarma, Ritumoni Information Theory In this article, we present a new class of codes known as row-column twisted Reed-Solomon codes (abbreviated as RCTRS), motivated by the works of \cite{beelen2017twisted} and \cite{liu2025column}. We explicitly provide conditions for such codes to be MDS and also ensure their existence. By determining the dimensions of their Schur squares, we prove that these MDS codes are not equivalent to Reed-Solomon codes, thus presenting a new family of non-RS MDS codes. Additionally, we prove that these MDS codes are also not equivalent to column twisted Reed-Solomon codes described in \cite{liu2025column}, showing the novelty of our construction. |
| title | Row-Column Twisted Reed-Solomon codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2509.06919 |