| In this paper, based on the graph state, we present a systematic way of constructinggood quantum codes, both additive and nonadditive, for systems with integer dimensions.With the help of computer search, which results in many interesting codes including somenonadditive codes meeting the Singleton bounds, we are able to construct explicitly fourfamilies of optimal codes, namely, [[6,2,3]]p, [[7,3,3]]p, [[8,2,4]]p and [[8,4,3]]p for anyodd dimension p and a family of nonadditive code ((5,p,3))p for arbitrary p > 3. In thecase of composite numbers as dimensions, we also construct a family of stabilizer codes((6,2·p2,3))2p for odd p, whose coding subspace is not of a dimension that is a power ofthe dimension of the physical subsystem. we have also try to constructed all the optimalstabilizer codes for d=3 by constructing the stabilizers of the code, some primal resultsare listed in this thesis.
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