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

This paper studied the construction for quantum code with parameters ((n, K, d)), 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.