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Example 5. The check matrix of Shor’s [[9 , 1 , 3]] code is 

<img src='content_image/311298.jpg'>

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. 

<img src='content_image/311299.jpg'>

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