Construction and enumeration for self-dual cyclic codes of even length over $\mathbb{F}_{2^m} + u\mathbb{F}_{2^m}$
| Autor: | Cao, Yuan, Cao, Yonglin, Dinh, Hai Q., Fu, Fang-Wei, Ma, Fanghui |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$, $R=\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}$ $(u^2=0)$ and $s,n$ be positive integers such that $n$ is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite chain ring $R$ of length $2^sn$ and provide a calculation method to obtain all distinct codes. Moreover, we obtain a clear formula to count the number of all these self-dual cyclic codes. As an application, self-dual and $2$-quasi-cyclic codes over $\mathbb{F}_{2^m}$ of length $2^{s+1}n$ can be obtained from self-dual cyclic code over $R$ of length $2^sn$ and by a Gray map preserving orthogonality and distances from $R$ onto $\mathbb{F}_{2^m}^2$. Comment: arXiv admin note: text overlap with arXiv:1811.11018, arXiv:1907.07107 |
| Databáze: | arXiv |
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