If entanglement is available, the error-correcting ability of quantum codescan be increased. We show how to optimize the minimum distance of anentanglement-assisted quantum error-correcting (EAQEC) code, obtained by addingebits to a standard quantum error-correcting code, over different encodingoperators. By this encoding optimization procedure, we found several new EAQECcodes, including a family of [[n, 1, n; n-1]] EAQEC codes for n odd and codeparameters [[7, 1, 5; 2]], [[7, 1, 5; 3]], [[9, 1, 7; 4]], [[9, 1, 7; 5]],which saturate the quantum singleton bound for EAQEC codes. A random searchalgorithm for the encoding optimization procedure is also proposed.
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