Lee Distance of cyclic codes of length $2^ς$ over $\mathbb{F}_{2^m} + u\mathbb{F}_{2^m} + u^2\mathbb{F}_{2^m}$
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918135653728256 |
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| author | Acharya, Divya Poojary, Prasanna R, Vadiraja Bhatta G |
| author_facet | Acharya, Divya Poojary, Prasanna R, Vadiraja Bhatta G |
| contents | Let $p$ be a prime number and $ς$ and $m$ be a positive integers. Let $\mathcal{R} = \mathbb{F}_{2^m} + u\mathbb{F}_{2^m} + u^2\mathbb{F}_{2^m}$ ($u^3 = 0$). Cyclic codes of length $2^ς$ over $\mathcal{R}$ are precisely the ideals of the local ring $\frac{\mathcal{R}[x]}{\langle x^{2^ς}-1 \rangle}$. The Gray map from a code of Lee weight over $\mathbb{Z}_4$ to a code with Hamming weight over $\mathbb{F}_2$ is known to preserve weight. In this paper, we determine the Lee distance of cyclic codes of length $2^ς$ over $\mathcal{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lee Distance of cyclic codes of length $2^ς$ over $\mathbb{F}_{2^m} + u\mathbb{F}_{2^m} + u^2\mathbb{F}_{2^m}$ Acharya, Divya Poojary, Prasanna R, Vadiraja Bhatta G Combinatorics Let $p$ be a prime number and $ς$ and $m$ be a positive integers. Let $\mathcal{R} = \mathbb{F}_{2^m} + u\mathbb{F}_{2^m} + u^2\mathbb{F}_{2^m}$ ($u^3 = 0$). Cyclic codes of length $2^ς$ over $\mathcal{R}$ are precisely the ideals of the local ring $\frac{\mathcal{R}[x]}{\langle x^{2^ς}-1 \rangle}$. The Gray map from a code of Lee weight over $\mathbb{Z}_4$ to a code with Hamming weight over $\mathbb{F}_2$ is known to preserve weight. In this paper, we determine the Lee distance of cyclic codes of length $2^ς$ over $\mathcal{R}$. |
| title | Lee Distance of cyclic codes of length $2^ς$ over $\mathbb{F}_{2^m} + u\mathbb{F}_{2^m} + u^2\mathbb{F}_{2^m}$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.03911 |