Cyclic orbit flag codes

In network coding, a flag code is set of sequences nested subspaces $${{\mathbb {F}}}_q^n$$ , being {F}}}_q$$ the finite field with q elements. Flag codes defined as orbits cyclic subgroup general linear group acting on flags are called orbit codes. Inspired by ideas in Gluesing-Luerssen et al. (Adv Math Commun 9(2):177–197, 2015), we determine cardinality and provide bounds for its distance help largest subfield over which all vector spaces (the best friend flag). Special attention paid to two specific families attaining extreme possible values distance: Galois optimum We study detail both classes analyze parameters respective subcodes that still have orbital structure.