Let $n$ be a positive integer with a factor $k$ such that $n\ge 3k$. Let $q$ be a prime power, and let ${\mathcal{G}}_q(n,k)$ be the set of all $k$-dimensional ${\mathbb{F}}_q$-subspaces of the field ${\mathbb{F}}_{q^n}$. In this paper, we construct cyclic subspace codes in ${\mathcal{G}}_q(n,k)$ with minimum distance $2k-2$ and size $(\lceil \frac{n}{2k}\rceil -1)\cdot \frac{(q^n-1)q^k}{q-1}$. In the case $n=3k$, their sizes differ from the sphere-packing bound for subspace codes by a factor of $\frac{1}{q-1}$ asymptotically as $k$ goes to infinity. Our construction makes use of variants of the Sidon spaces constructed by Roth et al. (2018) and analogous to the results they attained for the case $n=2k$. We also establish the existence of Sidon spaces of ${\mathcal{G}}_q(7k,2k)$, and thus we resolve part of the conjecture about the existence of cyclic subspace codes in ${\mathcal{G}}_q(n,k)$ with minimum distance $2k-2$ and size $\frac{q^n-1}{q-1}$.

让 $ñ$ 是一个带因子的正整数 $ķ$ 这样 $ñ\ge 3ķ$。让$q$ 成为主要力量，让 ${\mathcal{G}}_q（ñ，ķ）$ 成为所有人的集合 $ķ$尺寸 ${\mathbb{F}}_q$-字段的子空间 ${\mathbb{F}}_{q^{ñ}}$。在本文中，我们构造了循环子空间代码${\mathcal{G}}_q（ñ，ķ）$ 最小距离 $2ķ-2$ 和大小 $（\lceil \frac{ñ}{2ķ}\rceil -\mathrm{1个}）\cdot \frac{（q^{ñ}-\mathrm{1个}）q^{ķ}}{q-\mathrm{1个}}$。在这种情况下$ñ=3ķ$，其大小与子空间代码的球面填充边界相差一个因子 $\frac{\mathrm{1个}}{q-\mathrm{1个}}$ 渐近地 $ķ$去无穷大。我们的构造利用了Roth等人构造的Sidon空间的变体。（2018）并类似于他们为该案获得的结果$ñ=2ķ$。我们还建立了Sidon空间的存在${\mathcal{G}}_q（7ķ，2ķ）$，因此我们解决了关于子空间中循环子空间码的存在的部分猜想 ${\mathcal{G}}_q（ñ，ķ）$ 最小距离 $2ķ-2$ 和大小 $\frac{q^{ñ}-\mathrm{1个}}{q-\mathrm{1个}}$。