Parallel construction for constant dimension codes from mixed dimension construction

The article delves into the advanced topic of constant dimension codes, focusing on a new parallel construction method derived from mixed dimension constructions. By replacing restricted rank-metric codes with maximum rank-distance codes, the authors achieve substantial improvements in the size and efficiency of these codes. The research builds upon existing constructions, such as the mixed dimension construction proposed by Lao et al., and presents several new lower bounds that outperform previously known results. The article is structured to provide a comprehensive overview of the topic, including a review of previous known results, basic definitions, and the detailed derivation of the new construction method. The authors also discuss the implications of their findings and highlight the potential for further advancements in the field.