Combining Parallel Linkage Construction and Echelon-Ferrers Construction for Constant-Dimension Codes

Abstract

In the constant dimension codes (CDCs) case, to explore the largest possible value 𝒜_q(n, d, k) is one of the most fundamental topics in subspace coding. Echelon-Ferrers is an approach proposed in 2009 for CDCs’ construction, and has received extensive attentions. In this letter, in order to further improve the constructions, we study the method which combines linkage construction and echelon-Ferrers construction. This allows us to produce some improvements to lower bounds for constant dimension codes, including 𝒜_q(13,4,4), 𝒜_q(17, 4, 4), 𝒜_q(19, 6, 6) etc.