Abstract
One of the most fundamental topics in subspace coding is to explore the maximal possible value \(\mathbf{A}_q(n,d,k)\) of a set of k-dimensional subspaces in \(\mathbb F_q^n\) such that the subspace distance satisfies \(\text {d}_{\text {S}}(U,V) = \dim (U+V)-\dim (U\cap V) \ge d\) for any two different k-dimensional subspaces U and V in this set. In this paper, we propose a construction for constant dimension subspace codes from the existing results. This construction is done by merging two existing constructions, which exceeds the latest improvements including the cases: \(A_2(8,4,3)\ge 1331\) and \(A_2(8,4,4)\ge 4802\).
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Acknowledgement
The work is supported by the Science and Technology Planning Project of Guangdong Province (No. 190827105555406, 2019B010116001), the Natural Science Foundation of Guangdong Province (No. 2020A1515010899), the Key Scientific Research Project of Universities in Guangdong Province (No. 2020ZDZX3028), the innovation strong school project of Guangdong Province (No. 2020K2D2X1201) and the Natural Science Foundation of China (NO.61672303,61872083,61872081).
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Zhou, K., Chen, Y., Zhang, Z., Shi, F., He, X. (2021). A Construction for Constant Dimension Codes from the Known Codes. In: Liu, Z., Wu, F., Das, S.K. (eds) Wireless Algorithms, Systems, and Applications. WASA 2021. Lecture Notes in Computer Science(), vol 12937. Springer, Cham. https://doi.org/10.1007/978-3-030-85928-2_20
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