Abstract Given $${{\mathbb {F}}}_q$$ F q the finite field of size q, a flag code on $${{\mathbb {F}}}_q^n$$ F q n consists of a set of flags with a fixed sequence of dimensions (the type). In this paper, we deal with cyclic orbit flag codes, that are orbits of a Singer cycle of the general linear group acting on flags on $${{\mathbb {F}}}_q^n$$ F q n . Inspired by the results in Gluesing-Luerssen and Lehmann (Des Codes Crypt 89:447–470, 2021) and Roth et al. (IEEE Trans Inf Theory 64(6):4412–4422, 2018) about cyclic orbit codes, we completely characterize those cyclic orbit flag codes attaining the best distance for the largest possible orbit size, that is, optimal full-length cyclic orbit flag codes. Finally, we show that the distance distribution of this family of codes depends only on q, n and the type of the generating flag, also addressing the case of a union of orbits.

In the context of network coding, a flag code is a set of flags, i.e., sequences of nested subspaces of$\mathbb{F}_{q}^{n}$, being$\mathbb{F}_{q}$the finite field of size$q$• The general linear group acts on the flag variety and orbits of this action are called orbit flag codes. In particular, if the acting subgroup is cyclic, we speak about cyclic orbit flag codes. Following the results in [10] and [15] about cyclic orbit (subspace) codes, we study cyclic orbit flag codes attaining both the best possible size and distance, that is, optimal full-length cyclic orbit flag codes and characterize them in terms of the generating flag. We also analyze flag codes obtained as union of these cyclic orbits.