Optimum Distance Flag Codes from Spreads via Perfect Matchings in Graphs
Abstract
In this paper, we study flag codes on the vector space Fqn, being q a prime power and Fq 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 Fqn. 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.
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