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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.05317 |
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| _version_ | 1866915433575088128 |
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| author | Ouagagui, S. Benbelkacem, N. Batoul, A. Abualrub, T. |
| author_facet | Ouagagui, S. Benbelkacem, N. Batoul, A. Abualrub, T. |
| contents | In this paper, we investigate the structure and properties of additive complementary dual (ACD) codes over the mixed alphabet $\mathbb{F}_2\mathbb{F}_4$ relative to a certain inner product defined over $\mathbb{F}_2\mathbb{F}_4$. We establish sufficient conditions under which such codes are additive complementary dual (ACD) codes. We also show that ACD codes over $\mathbb{F}_{2}\mathbb{F}_{4}$ can be applied to construct binary linear complementary dual codes as their images under the linear map $W$. Notably, we prove that if the binary image of a code is LCD, then the original code is necessarily ACD. An example is given where the image is a distance-optimal binary LCD code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{F}_{2}\mathbb{F}_{4}$-Additive Complementary Dual Codes Ouagagui, S. Benbelkacem, N. Batoul, A. Abualrub, T. Information Theory In this paper, we investigate the structure and properties of additive complementary dual (ACD) codes over the mixed alphabet $\mathbb{F}_2\mathbb{F}_4$ relative to a certain inner product defined over $\mathbb{F}_2\mathbb{F}_4$. We establish sufficient conditions under which such codes are additive complementary dual (ACD) codes. We also show that ACD codes over $\mathbb{F}_{2}\mathbb{F}_{4}$ can be applied to construct binary linear complementary dual codes as their images under the linear map $W$. Notably, we prove that if the binary image of a code is LCD, then the original code is necessarily ACD. An example is given where the image is a distance-optimal binary LCD code. |
| title | $\mathbb{F}_{2}\mathbb{F}_{4}$-Additive Complementary Dual Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2508.05317 |