Parallel sub-code construction for constant-dimension codes

Due to the prior work by Köetter and Kschischang (IEEE Trans Inf Theory 54(8):3579–3591, 2008), subspace codes (especially constant-dimension codes, CDC for short) have attracted significant attention in recent years. The sub-code construction is currently one of the most popular constructions, which can be used to further improve the lower bounds for CDCs’ construction. In this paper, we show how to improve the construction of subspace codes from two parallel versions of the sub-code construction. This construction allows us to obtain larger size codes for a given minimum distance, which exceeds the latest improvements on the sub-code construction (Cossidente et al. in Adv Math Commun, 2021, https://doi.org/10.3934/amc.2021007 ; Lao et al. in Cryptogr Commun, 2021) in the cases including 𝒜_q(10,4,5), 𝒜_q(14,6,7) , and 𝒜_q(16,8,8) , etc.