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.