New Quantum MDS Codes

New quantum maximum-distance-separable (MDS) codes with parameters [[<i>q</i><sup>2</sup> + 1, <i>q</i><sup>2</sup> -2<i>d</i> + 3, <i>d</i>]]<sub>q</sub>, where <i>q</i>=2<sup>t</sup>, <i>t</i> ≥ 1 and 3 ≤ <i>d</i> ≤ <i>q</i>+1 is an odd integer, are constructed in this paper.

[1]  M. Hamada.  Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction , 2008, IEEE Transactions on Information Theory.

[2]  Pradeep Kiran Sarvepalli,et al.  On Quantum and Classical BCH Codes , 2006, IEEE Transactions on Information Theory.

[3]  Laflamme,et al.  Perfect Quantum Error Correcting Code. , 1996, Physical review letters.

[4]  H. Chau.  Five quantum register error correction code for higher spin systems , 1997, quant-ph/9702033.

[5]  Zongben Xu,et al.  On [[n,n-4,3]]q Quantum MDS Codes for odd prime power q , 2009, ArXiv.

[6]  Y. Edel,et al.  Quantum twisted codes , 2000 .

[7]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[8]  Pradeep Kiran Sarvepalli,et al.  Nonbinary quantum Reed-Muller codes , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[9]  Alexei E. Ashikhmin,et al.  Nonbinary quantum stabilizer codes , 2001, IEEE Trans. Inf. Theory.

[10]  F. Lemmermeyer.  Error-correcting Codes , 2005 .

[11]  Martin Rötteler,et al.  On quantum MDS codes , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[12]  Keqin Feng,et al.  Quantum Codes and Exist , 2002 .

[13]  Santosh Kumar,et al.  Nonbinary Stabilizer Codes Over Finite Fields , 2005, IEEE Transactions on Information Theory.

[14]  Qing Chen,et al.  Graphical Nonbinary Quantum Error-Correcting Codes , 2008 .

[15]  T. Beth,et al.  On optimal quantum codes , 2003, quant-ph/0312164.

[16]  Shor,et al.  Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[17]  N. J. A. Sloane,et al.  Quantum Error Correction Via Codes Over GF(4) , 1998, IEEE Trans. Inf. Theory.

[18]  Eric M. Rains.  Nonbinary quantum codes , 1999, IEEE Trans. Inf. Theory.

[19]  Andrew M. Steane.  Enlargement of Calderbank-Shor-Steane quantum codes , 1999, IEEE Trans. Inf. Theory.

[20]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[21]  A. Calderbank,et al.  Quantum Error Correction and Orthogonal Geometry , 1996, quant-ph/9605005.