Automorphism Groups and Isometries for Cyclic Orbit Codes

Abstract

We study orbit codes in the field extension F q n . First we show that the automorphism group of a cyclic orbit code is contained in the normalizer of the Singer subgroup if the orbit is generated by a subspace that is not contained in a proper subfield of F q n . We then generalize to orbits under the normalizer of the Singer subgroup. In that situation some exceptional cases arise and some open cases remain. Finally we characterize linear isometries between such codes.

Multi-Sidon spaces over finite fields

“…In [31] Horlemann-Trautmann initiated the study of the equivalence for subspace codes in a very general context. More recently in [15] Gluesing-Luerssen and Lehmann investigate the case of cyclic orbit codes, that is G-orbits of a subspace U of F q n with G a Singer cycle of GL(n, q). Therefore, motivated by [15,Theorem 2.4] and according to [15, Definition 3.5], we say that two cyclic subspace codes C U and C V are linearly equivalent if there exists i ∈ {0, .…”