Generalized orbital construction of optimum distance flag codes

Subspace coding is a fundamental technique for reliable communication in random linear network coding. In the multishot scenario, flag codes extend this structure by encoding information in sequences of nested subspaces. In this paper, we study the construction of optimum distance flag codes (ODFCs) via group actions. Starting from k -dimensional orbit subspace codes with maximum distance in F q r k , for r ≥ 2 we analyze how the associated group action can be lifted to the flag variety of a certain type vector. Our approach provides explicit orbital constructions of flag codes of a particular type vector whose cardinality attains the largest value allowed by known bounds. The resulting codes inherit the orbital structure of k -dimensional subspace codes, which simplifies the analysis of their size and distance. Moreover, the number of orbits required to attain the maximum cardinality is determined by the divisibility of q k − 1 by r . Thus, our work generalizes the orbital construction of ODFCs in [4] under a certain restriction on type vector.