Generalized Deutsch-Jozsa (DJ) problem proposed by Qiu et al. in 2016 is a generalization of the DJ problem, which can be described as a symmetric partial Boolean function $$\text{ DJ}_n^k : \{0,1\}^n\rightarrow \{0,1\}$$ defined as $$\text{ DJ}_n^k(x)=1$$ for $$|x|=n/2$$ , $$\text{ DJ}_n^k(x)=0$$ for |x| in the set $$\{0,1,\ldots ,k,n-k,n-k+1,\ldots ,n\}$$ , and it is undefined for the rest cases, where n is even, $$0\le k