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number of loops, N$_{avg}$ , to obtain these parameters (which we estimate by performing the algorithm 10 4 times for each c ). Note that N$_{avg}$ is close to 2 2 $^{ck}$N ( r, c ) /N$_{opt}$ for the [[7 , 1 , 3]] quantum BCH code, except for the case c = 2, where N$_{avg}$ is about half of 2 2 $^{ck}$N ( r, c ) /N$_{opt}$ . For Shor’s [[9 , 1 , 3]] code, N$_{avg}$ is much less than 2 2 $^{ck}$N ( r, c ) /N$_{opt}$ in most cases. 

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✷ 

Example 7. We applied the random search algorithm to a standard [[15 , 7 , 3]] quantum BCH code and the results are shown in Table 7. Note that we did not find the fully optimized 

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parameters in this case, since the complexity is very high. However, compared with the [[15 , 3 , 5; 4]] EAQEC code, obtained by the construction of (19) from a [15 , 7 , 5] classical 

