Subspace codes, especially cyclic constant subspace codes, are of great use in random network coding. Subspace codes can be constructed by subspaces and subspace polynomials. In particular, many researchers are keen to find special subspaces and subspace polynomials to construct subspace codes with the size and the minimum distance as large as possible. In [14], Roth, Raviv and Tamo constructed several subspace codes using Sidon spaces, and it is proved that subspace codes constructed by Sidon spaces has the largest size and minimum distance. In [12], Niu, Yue and Wu extended some results of [14] and obtained several new subspace codes. In this paper, we first provide a sufficient condition for the sum of Sidon spaces is again a Sidon space. Based on this result, we obtain new cyclic constant subspace codes through the sum of two and three Sidon spaces. Our results generalize the results in [14] and [12].
翻译：子空间代码,特别是环常次空间代码,在随机网络编码中非常有用。子空间代码可以由子空间和子空间多元度构建。特别是,许多研究人员渴望找到特殊的子空间和子空间多元度代码,以尽可能大和最小距离构建子空间代码。在 [14] 中,罗斯、拉维夫和塔莫利用西顿空间构建了几个子空间代码,并证明西顿空间构建的子空间代码有最大的大小和最小距离。在 [12] 、 纽、 岳和吴中,子空间代码扩展了一些(14)的结果,并获得了几个新的子空间代码。在本文中,我们首先为西顿空间的总和提供了充分的条件。在此基础上,我们通过两个和三个西顿空间的总和,获得了新的环常次空间代码。我们的结果概括了在 [14] 和 [12] 中的结果。
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