Disproving some theorems in Sharma and Chauhan et al. (2018, 2021)
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916644579704832 |
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| author | Takieldin, Ramy Solé, Patrick |
| author_facet | Takieldin, Ramy Solé, Patrick |
| contents | The main objective of this work is to show, through counterexamples, that some of the theorems presented in the papers of Sharma \textit{et al.} (2018) and Chauhan \textit{et al.} ( 2021) are incorrect. Although they used these theorems to establish a sufficient condition for a multi-twisted (MT) code to be linear complementary dual (LCD), we show that this condition itself remains valid. We further improve this condition by removing the restrictions on the shift constants and relaxing the required coprimality condition. We show that compared to the previous condition, the modified condition is able to identify more LCD MT codes. Furthermore, without the need for a normalized set of generators, we develop a formula to determine the dimension of any $ρ$-generator MT code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Disproving some theorems in Sharma and Chauhan et al. (2018, 2021) Takieldin, Ramy Solé, Patrick Information Theory The main objective of this work is to show, through counterexamples, that some of the theorems presented in the papers of Sharma \textit{et al.} (2018) and Chauhan \textit{et al.} ( 2021) are incorrect. Although they used these theorems to establish a sufficient condition for a multi-twisted (MT) code to be linear complementary dual (LCD), we show that this condition itself remains valid. We further improve this condition by removing the restrictions on the shift constants and relaxing the required coprimality condition. We show that compared to the previous condition, the modified condition is able to identify more LCD MT codes. Furthermore, without the need for a normalized set of generators, we develop a formula to determine the dimension of any $ρ$-generator MT code. |
| title | Disproving some theorems in Sharma and Chauhan et al. (2018, 2021) |
| topic | Information Theory |
| url | https://arxiv.org/abs/2503.03762 |