Distance Distributions of Cyclic Orbit Codes

The distance distribution of a code is the vector whose ith entry number pairs codewords with i. We investigate structure for cyclic orbit codes, which are subspace codes generated by action $${\mathbb {F}}_{q^n}^*$$ on an {F}}_q$$ -subspace U {F}}_{q^n}$$ . Note that Singer cycle in general linear group all -automorphisms show full-length maximal possible depends only $$q,\,n$$ , and dimension U. For lower minimum distance, we provide partial results towards characterization distribution, especially case any two intersect space at most 2. Finally, briefly address union maximum distance.