标题： 从斯坦纳系统得到的直径完美等重码族 显示英文标题

标题： A family of diameter perfect constant-weight codes from Steiner systems

摘要： If $S$ is a transitive metric space, then $|C|\cdot|A| \le |S|$ for any distance-$d$ code $C$ and a set $A$, ``anticode'', of diameter less than $d$. 对于每个Steiner S$(t,k,n)$系统$S$，我们证明存在一个$q$-元恒重码$C$，长度为~$n$，重量~$k$（或$n-k$），距离$d=2k-t+1$（分别地，$d=n-t+1$）和一个直径为$d-1$的反码$A$，使得对偶$(C,A)$达到码-反码界，且$C$的码字的支撑集是$S$的块（分别地，$S$的块的补集）。 我们研究了估计存在这样的码的$q$的最小值的问题，并找到了$t$的小值的最小值。 关键词：直径完美码，反码，等重码，码-反码界，斯坦纳系统。 显示英文摘要

摘要： If $S$ is a transitive metric space, then $|C|\cdot|A| \le |S|$ for any distance-$d$ code $C$ and a set $A$, ``anticode'', of diameter less than $d$. For every Steiner S$(t,k,n)$ system $S$, we show the existence of a $q$-ary constant-weight code $C$ of length~$n$, weight~$k$ (or $n-k$), and distance $d=2k-t+1$ (respectively, $d=n-t+1$) and an anticode $A$ of diameter $d-1$ such that the pair $(C,A)$ attains the code--anticode bound and the supports of the codewords of $C$ are the blocks of $S$ (respectively, the complements of the blocks of $S$). We study the problem of estimating the minimum value of $q$ for which such a code exists, and find that minimum for small values of $t$. Keywords: diameter perfect codes, anticodes, constant-weight codes, code--anticode bound, Steiner systems.