On the Construction for Quantum Code ((n,K,d))_p via Logic Function over F_p

This paper studied the construction for quantum code with parameters ((n, K, d))_p by use of an n-variable logic function with APC distance d´ ¿ 2 over F_p. We discussed the parameters of the constructed quantum codes, then obtained d ¿ d´ and the maximal K for all d = d´ - k, 0 ¿ k ¿ d´ - 2. It was also discussed the basic states and the equivalent conditions of meeting quantum Singleton bound in this paper. With our result, for a given function wit APC distance d´ ¿ 2, we can construct quantum codes with the minimum distance d = d´- k for all 0 ¿ k ¿ d´- 2 and presented the basic states of the constructed codes.