线性码的Chow定理
Chow's theorem for linear codes
摘要：
设$Γ_{k}(V)$是由$q$元素和$1<k<n-1$组成的有限域${\mathbb F}_{q}$上的$n$维向量空间的$k$维子空间构成的Grassmann图.用$Γ(n,k)_q$表示Grassmann图对所有非退化线性$[n,k]_q$码的限制。我们描述了图$Γ(n,k)_q$的极大团，并证明了该图的每一个自同构都是由$V$的单项半线性自同构导出的。
英文摘要：
Let $Γ_{k}(V)$ be the Grassmann graph formed by $k$-dimensional subspaces of an $n$-dimensional vector space over the finite field ${\mathbb F}_{q}$ consisting of $q$ elements and $1<k<n-1$. Denote by $Γ(n,k)_q$ the restriction of the Grassmann graph to the set of all non-degenerate linear $[n,k]_q$ codes. We describe maximal cliques of the graph $Γ(n,k)_q$ and show that every automorphism of this graph is induced by a monomial semilinear automorphism of $V$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
