Let $C$ be a two and three-weight ternary code. Furthermore, we assume that $C_\ell$ are $t$-designs for all $\ell$ by the Assmus--Mattson theorem. We show that $t \leq 5$. As a corollary, we provide a new characterization of the (extended) ternary Golay code.

翻译：设$C$是一个两重量和三重量的三元码。进一步，我们假设根据Assmus-Mattson定理，对于所有$\ell$，$C_\ell$是$t$-设计。我们证明$t \leq 5$。作为推论，我们给出了（扩展的）三元Golay码的一个新刻画。