Optimum distance flag codes from spreads via perfect matchings in graphs

In this paper, we study flag codes on the vector space $${{\mathbb {F}}}_q^n$$ F q n , being q a prime power and $${{\mathbb {F}}}_q$$ F q the finite field of q elements. More precisely, we focus on flag codes that attain the maximum possible distance (optimum distance flag codes) and can be obtained from a spread of $${{\mathbb {F}}}_q^n$$ F q n . We characterize the set of admissible type vectors for this family of flag codes and also provide a construction of them based on well-known results about perfect matchings in graphs. This construction attains both the maximum distance for its type vector and the largest possible cardinality for that distance.