New constant dimension subspace codes from multilevel linkage construction (Q6584303)

The problem of finding large constant dimension subspace codes (CDCs) is an active area of research. One major technique is to construct these codes by lifting rank-metric codes. One class of rank-metric codes that has been used in this way are the Ferrers diagram rank-metric codes. Etzion and Silberstein have described a multilevel construction for CDCs based on these codes [\textit{T. Etzion} and \textit{N. Silberstein}, IEEE Trans. Inf. Theory 55, No. 7, 2909--2919 (2009; Zbl 1367.94414)]. These ideas are further developed by \textit{N. Silberstein} and \textit{A.-L. Trautmann} [IEEE Trans. Inf. Theory 61, No. 7, 3937--3953 (2015; Zbl 1359.94834)].\N\NThe authors of this article introduce a variation of these codes that they call rank-restricted Ferrers diagram rank-metric (RFDRM) codes and describe a way to construct them. They present what they call a multilevel linkage construction for CDCs that combines ideas from the construction of Etzion and Silberstein with a construction from a recent paper of \textit{A. Cossidente} et al. [Adv. Math. Commun. 17, No. 3, 536--550 (2023; Zbl 1525.94067)]. The authors explain how using lifted RFDRM codes in this construction leads to new CDCs that have sizes improving on the best-known bounds in many cases.