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首页> 外文期刊>IEEE Transactions on Information Theory >$BBZ_{2}BBZ_{4}$ -Additive Cyclic Codes
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$BBZ_{2}BBZ_{4}$ -Additive Cyclic Codes

机译：$ BBZ_ {2} BBZ_ {4} $-附加循环码

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摘要

In this paper, we study $BBZ_{2}BBZ_{4}$-additive cyclic codes. These codes are identified as $BBZ_{4}[x]$-submodules of the ring $R_{r,s}=BBZ_{2}[x]/langle x^{r}-1rangletimesBBZ_{4}left[xright]/langle x^{s}-1rangle$. The algebraic structure of this family of codes is studied and a set of generator polynomials for this family as a $BBZ_{4}[x]$-submodule of the ring $R_{r,s}$ is determined. We show that the duals of $BBZ_{2}BBZ_{4}$-additive cyclic codes are also cyclic. We also present an infinite family of Maximum Distance separable with respect to the singleton bound codes. Finally, we obtain a number of binary linear codes with optimal parameters from the $BBZ_{2}BBZ_{4}$-additive cyclic codes.
机译：在本文中，我们研究了$ BBZ_ {2} BBZ_ {4} $可加循环码。这些代码被标识为$ R_ {r，s} = BBZ_ {2} [x] / langle x ^ {r} -1rangletimesBBZ_ {4} left [xright]的$ BBZ_ {4} [x] $-子模块/ langle x ^ {s} -1rangle $。研究了该代码族的代数结构，并确定了该族的一组生成多项式作为环$ R_ {r，s} $的$ BBZ_ {4} [x] $子模块。我们证明，$ BBZ_ {2} BBZ_ {4} $加性循环码的对偶也是循环的。我们还提出了关于单例绑定代码可分离的无限距离的最大距离。最后，我们从$ BBZ_ {2} BBZ_ {4} $可加循环码中获得一些具有最佳参数的二进制线性码。

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