Does there exist a combinational TSC checker for 1/3 code using only primitive gates?

The answer is "no." For gate-level circuits and single stuck-at faults, it has been shown that all m/n-code TSC checkers can be successfully designed, except one for 1/3 code. Although many researchers believe such a checker does not exist, none has proved that this is the case, which makes the problem open. In this paper, we show that no such checker exists using only AND, OR, and NOT gates (and, therefore, NAND and NOR gates). We solve this problem by giving a strict and clear proof. We also can deduce from our proof that no such TSC checker exists for any code which has only three code words.