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

代码的距离分布是向量，向量的第i个条目是距离为i的代码字对的数量。我们研究循环轨道码的距离分布的结构，循环轨道码是由\（{\ mathbb {F}} _ {q ^ n} ^ * \）在\（{\ mathbb {F }} _ q \） -subspace ù的\（{\ mathbb {F}} _ {q ^ N} \）。注意，\（{\ mathbb {F}} _ {Q ^ N} ^ * \）是一般线性组中的某个歌手周期所有\（{\ mathbb {F}} _ q \）的-automorphisms  \（{ \ mathbb {F}} _ {q ^ n} \）。我们表明，对于具有最大可能距离的全长轨道代码，距离分布仅取决于\（q，\，n \）和U的尺寸 。对于具有较小最小距离的全长轨道代码，我们提供了部分结果，可用于描述距离分布，尤其是在任意两个码字在维数空间最大为2的情况下。具有最大距离的全长轨道代码的并集。