Abstract
AbstractIn 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.
Funder
Generalitat Valenciana
Ministerio de Ciencia, Innovación y Universidades
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics,Algebra and Number Theory
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