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. c d$_{opt}$ 2 2 $^{ck}$N ( r, c ) /N$_{opt}$ N$_{avg}$ 6 7 113.78 109.37 5 5 2.02 2.02 4 5 4.22 4.13 3 5 20.61 18.63 2 5 744 392.57 c d$_{opt}$ 2 2 $^{ck}$N ( r, c ) /N$_{opt}$ N$_{avg}$ 8 9 256 259.97 7 7 12.61 12.47 6 7 158.48 119.25 5 7 5600.63 1188.08 4 7 389393.94 7577.95 3 5 88.99 18.48 2 5 855.72 52.46 Table 6: Average number of trials of the random search algorithm on Shor’s [[9 , 1 , 3]] code Table 5: Average number of trials of the random search algorithm on the [[7 , 1 , 3]] quantum BCH code ✷ 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 c d$_{opt}$ d$_{std}$ 2 2 $^{ck}$N ( r, c ) 8 6 5-6 5 . 19 × 10 33 7 5 5-6 8 . 08 10 31 6 5 5-6 2 . 08 × 10 29 5 4 4-5 1 . 14 10 26 4 4 4-5 1 . 44 × 10 22 7 3 4 4 . 27 10 17 Table 7: Optimization over a [[15 , 7 , 3]] Quantum BCH code 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 32