Distance Distributions of Cyclic Orbit Codes

Automorphism groups and isometries for cyclic orbit codes

“…In [9] we studied the weight distribution of cyclic orbit codes. Some of the main results are summarized as follows.…”

“…For further details, e.g. on the actual values of the weight distribution, we refer to [9]. Recall from Remark 3.2 that the size of a cyclic orbit code is upper bounded by (q n − 1)/(q − 1).…”

“…First examples of cyclic orbit codes with good distance appeared already in [7], and in fact, in most of the literature, cyclic orbit codes have been studied in this setting, see for instance [10] for details on the orbit length and some distance results, [1,17,18,3,21] for constructions of unions of cyclic orbit codes with good distance with the aid of subspace polynomials and [9] for a study of the distance distribution of cyclic orbit codes. The aforementioned unions of cyclic orbit codes are in fact orbits codes under the normalizer of F * q n in GL n (q).…”

“…The nature of our counterexamples leads us to believe that the last statement does not need the assumption on δ s (U). We close the paper with an example where we list the number of distinct isometry classes of cyclic orbit codes and, making use of [9], also provide the weight distribution for each class.…”

Cyclic orbit flag codes

“…This family of codes has awaken a lot of interest due to the simplicity of their algebraic structure and to the existence of efficient encoding/decoding algorithms. We refer the reader to [5,6,8,9,10,19,21,23,24,26] for some of the more recent papers.…”