Example 5. The check matrix of Shor’s [[9 , 1 , 3]] code is As can be seen in Table 4, the parameters [[9 , 1 , 9; 8]], [[9 , 1 , 7; 5]] and [[9 , 1 , 7; 4]] achieve the quantum singleton bound for EAQECC (11) and are not equivalent to any standard quantum stabilizer code. A competing EAQEC code with n = 9 and d = 7 by the construction of [10] is a [[9 , 1 , 7; 6]] EAQEC code, obtained from a [9 , 2 , 7] linear quaternary code in Grassl’s table. Therefore, the [[9 , 1 , 7; 5]] and [[9 , 1 , 7; 4]] EAQEC codes are new. All the [[9 , 1 , 5; 2]], [[9 , 1 , 5; 3]], [[9 , 1 , 7; 4]], [[9 , 1 , 7; 5]] and [[9 , 1 , 7; 6]] codes are degenerate codes, and all the [[9 , 1 , 9; 8]] codes are nondegenerate codes, while the [[9 , 1 , 7; 7]] codes can be degenerate or nondegenerate. ✷      $^{000000000}$ 110000000 000000000 011000000 000000000 000110000 000000000 000011000 000000000 000000110 000000000 000000011 111111000 000000000 000111111 000000000       . c d$_{opt}$ d$_{std}$ N$_{opt}$ 2 2 $^{ck}$N ( r, c ) 8 9 7 256 65536 7 7 6 330624 4 . 17 × 10 6 6 7 6 278904 4 . 42 10 7 5 7 6 17748 9 . 94 × 10 7 4 7 5 132 5 . 14 10 7 3 5 5 69777 6 . 21 × 10 6 2 5 5 201 1 . 72 10 5 Table 4: Optimization over Shor’s [[9 , 1 , 3]] code 29