Uniqueness of Some Optimal Superimposed Codes

Four new results on the uniqueness of optimal superimposed codes are presented, namely, the uniqueness of $(w,r)$ superimposed codes of size $N\times T$ with $\displaystyle N=\binom{w+r+1}w$ and $T=w+r+1$ and the uniqueness of $(2,2)$ superimposed codes of size $18\times9$, $(2,2)$ superimposed codes of size $14\times7$, and $(3,3)$ superimposed codes of size $66\times11$.