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by a = 001110101110 with the simplified check matrix 

    $^{001110}$ 101110 000111 010111 100011 101011 110001 110101 111000 111010 011100 011101      . 

We call this the circulant construction of EAQEC codes, which is used for standard stabilizer codes in [18]. 

We examined the simplified check matrices cyclicly generated by every possible binary 2 n − tuple a by computer for n = 4 , · · · , 10 and r ≤ 2( n − 1). Parameters of EAQEC codes not equivalent to any standard quantum stabilizer codes are listed in Table 10. The parameters [[4 , 0 , 4; 2]], [[4 , 1 , 3; 1]], [[5 , 0 , 4; 2]], [[5 , 1 , 4; 3]], [[5 , 1 , 5; 4]], [[6 , 0 , 6; 4]], [[6 , 2 , 3; 1]], [[6 , 2 , 4; 3]], [[6 , 0 , 4; 1]], [[6 , 1 , 5; 4]], [[7 , 4 , 3; 2]], [[7 , 1 , 6; 5]], [[7 , 1 , 7; 6]], [[8 , 5 , 3; 2]], [[9 , 1 , 9; 8]], and [[10 , 0 , 10; 8]] also saturate the quantum singleton bound (11). 

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