Constructions of Constant Dimension Subspace Codes

05/23/2023

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by   Yun Li, et al.

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Subspace codes have important applications in random network coding. It is interesting to construct subspace codes with both sizes, and the minimum distances are as large as possible. In particular, cyclic constant dimension subspaces codes have additional properties which can be used to make encoding and decoding more efficient. In this paper, we construct large cyclic constant dimension subspace codes with minimum distances 2k-2 and 2k. These codes are contained in 𝒢_q(n, k), where 𝒢_q(n, k) denotes the set of all k-dimensional subspaces of 𝔽_q^n. Consequently, some results in <cit.>, <cit.>, and <cit.> are extended.