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.

如果S是传递度量空间，则$|C|\cdot |A|\le |S|$对于任何距离为 d 的代码C和直径小于d的集合A （“反码”） 。对于每个 Steiner S$（t,k,n）$系统S，我们证明存在一个长度为n 、重量为k（或$n-k$) 和距离$d=2k-t+1$（分别，$d=n-t+1$) 和直径的反码A$d-1$使得这对$（C,A）$达到码反码界，并且C的码字的支持是S的块（分别是S的块的补集）。我们研究了估计存在这样的代码的q最小值的问题，并找到了小t值的最小值。