Optimum Distance Cyclic H -Orbit Full Flag Codes

Flag codes, introduced as a special class of nested subspace codes, have recently attracted significant attention in the research community. In this work, we present constructions of optimum-distance cyclic H-orbit full flag codes, where H is a cyclic subgroup of F(q)(& lowast;)n of order at most q(n/2)+1 . Our aim is to extend certain results from (Horlemann-Trautmann and Rosenthal, 2018) to the framework of flag codes. The proposed constructions, unlike the work (Alonso-Gonz & aacute;lez and Navarro-P & eacute;rez, 2024), achieve full flags with optimum distance and either maximal or best-possible size, depending on the parity of the base field. We also provide explicit examples that demonstrate the structure of our codes. Furthermore, for the case of even base field size, we prove -via intricate arithmetical arguments- that our construction is unique under certain conditions.