Let $C$ be a four-weight binary code, which has all one vector. Furthermore, we assume that $C$ supports $t$-designs for all weights obtained from the Assmus--Mattson theorem. We previously showed that $t\leq 5$. In the present paper, we show an analogue of this result in the cases of five and six-weight codes.

翻译：设$C$是一个包含全1向量的四重量二进制码。进一步，我们假设$C$对所有通过Assmus--Mattson定理得到的重量支持t-设计。我们之前证明了$t\leq 5$。在本文中，我们展示了在五重量和六重量码情况下该结果的类似结论。