We call this the circulant construction of EAQEC codes, which is used for standard stabilizer codes in [18]. by a = 001110101110 with the simplified check matrix     $^{001110}$ 101110 000111 010111 100011 101011 110001 110101 111000 111010 011100 011101      . 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). n [[ n, k, d ; c ]] 4 [[4 , 0 , 4; 2]], [[4 , 1 , 3; 1]] 5 [[5 , 1 , 5; 4]], [[5 , 1 , 4; 3]], [[5 , 1 , 4; 2]], [[5 , 0 , 4; 2]], [[5 , 2 , 3; 2]] 6 [[6 , 0 , 6; 4]], [[6 , 1 , 5; 4]], [[6 , 1 , 4; 3]], [[6 , 2 , 4; 3]], [[6 , 0 , 4; 1]], [[6 , 2 , 3; 1]] 7 [[7 , 1 , 7; 6]], [[7 , 2 , 5; 5]], [[7 , 0 , 6; 4]], [[7 , 3 , 4; 4]],[[7 , 1 , 4; 2]], [[7 , 3 , 4; 3]], [[7 , 4 , 3; 2]] 8 [[8 , 0 , 8; 6]], [[8 , 1 , 6; 6]], [[8 , 0 , 6; 5]], [[8 , 2 , 6; 6]], [[8 , 1 , 6; 5]], [[8 , 0 , 6; 4]], [[8 , 3 , 5; 5]], [[8 , 2 , 5; 4]], [[8 , 1 , 4; 1]], [[8 , 3 , 4; 3]],[[8 , 5 , 3; 2]], 9 [[9 , 1 , 9; 8]], [[9 , 0 , 7; 6]], [[9 , 1 , 7; 6]], [[9 , 1 , 7; 7]], [[9 , 2 , 6; 6]], [[9 , 1 , 6; 5]], [[9 , 0 , 6; 4]], [[9 , 1 , 6; 6]], [[9 , 2 , 5; 4]], [[9 , 5 , 3; 1]], 10 [[10 , 0 , 10; 8]], [[10 , 1 , 8; 8]], [[10 , 0 , 8; 7]], [[10 , 0 , 8; 6]], [[10 , 0 , 7; 5]], [[10 , 1 , 7; 6]], [[10 , 2 , 7; 7]], [[10 , 1 , 6; 5]], [[10 , 3 , 6; 7]], [[10 , 0 , 6; 3]], [[10 , 3 , 6; 6]], [[10 , 2 , 6; 5]], [[10 , 1 , 6; 4]], [[10 , 4 , 5; 5]], [[10 , 2 , 5; 2]], [[10 , 4 , 5; 4]], [[10 , 2 , 5; 3]], Table 10: Parameters of [[ n, k, d ; c ]] EAQEC codes not equivalent to any standard [[ n + c, k ]] codes. 35