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For each odd prime power $q$, let $4 \leq n\leq q^{2}+1$. Hermitianself-orthogonal $[n,2,n-1]$ codes over $GF(q^{2})$ with dual distance three areconstructed by using finite field theory. Hence, $[[n,n-4,3]]_{q}$ quantum MDScodes for $4 \leq n\leq q^{2}+1$ are obtained.

On $[[n,n-4,3]]_{q}$ Quantum MDS Codes for odd prime power $q$