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$C$为一个包含全1向量的四重量二元码。进一步假设$C$支撑由Assmus-Mattson定理得到的所有重量对应的$t$-设计。我们此前已证明$t\leq 5$。本文给出五重量与六重量码情形下该结果的类似结论。