Optimum Distance Cyclic H-Orbit Full Flag Codes
IEEE Access, cilt.13, ss.194149-194155, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 13
- Basım Tarihi: 2025
- Doi Numarası: 10.1109/access.2025.3631971
- Dergi Adı: IEEE Access
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
- Sayfa Sayıları: ss.194149-194155
- Anahtar Kelimeler: Codes, Orbits, Video recording, Network coding, Vectors, Space vehicles, Electronic mail, Galois fields, Extraterrestrial measurements, Upper bound, Flag codes, orbit flag codes, subspace codes
- Kırklareli Üniversitesi Adresli: Evet
Özet
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∗ qn of order at most qn/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-González and Navarro-Pérez, 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.