Quantum codes from cyclic codes over the ring Fp[u]/〈u3 − u〉

In this paper, we study nonbinary quantum codes from cyclic codes over the ring Fp[u]/〈u3 − u〉 for odd prime p. We give the constructional properties of linear and cyclic codes over the ring Fp[u]/...

[1]  On quantum codes obtained from cyclic codes over 𝔽2 + u𝔽2 + u2𝔽2 , 2018 .

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

[3]  Steane,et al.  Simple quantum error-correcting codes. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[4]  Xueliang Li,et al.  Binary Construction of Quantum Codes of Minimum Distance Three and Four , 2004, IEEE Trans. Inf. Theory.

[5]  Irfan Siap,et al.  ON QUANTUM CODES FROM CYCLIC CODES OVER A CLASS OF NONCHAIN RINGS , 2016 .

[6]  Chaoping Xing,et al.  Asymptotic bounds on quantum codes from algebraic geometry codes , 2006, IEEE Transactions on Information Theory.

[7]  Jianfa Qian.  Quantum Codes from Cyclic Codes over $F_2+vF_2$ , 2013 .

[8]  Mohammad Ashraf,et al.  Quantum codes from cyclic codes over $$F_q+uF_q+vF_q+uvF_q$$Fq+uFq+vFq+uvFq , 2016, Quantum Inf. Process..

[9]  Shixin Zhu,et al.  QUATERNARY CONSTRUCTION OF QUANTUM CODES FROM CYCLIC CODES OVER $\mathbb{F}_4 + u\mathbb{F}_4$ , 2011 .

[10]  Shanlin Yang,et al.  Good p-ary quasic-cyclic codes from cyclic codes over $$\mathbb{F}_p + v\mathbb{F}_p$$ , 2012, J. Syst. Sci. Complex..

[11]  D. Gottesman.  An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation , 2009, 0904.2557.

[12]  Jian Gao.  Quantum codes from cyclic codes over q+vq+v2q+v3q , 2015 .

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

[14]  Yasemin Cengellenmis,et al.  On quantum codes obtained from cyclic codes over A2 , 2015 .

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

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

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

[18]  Reginaldo Palazzo Júnior,et al.  Constructions of new families of nonbinary CSS codes , 2010, Discret. Math..

[19]  Mohammad Ashraf,et al.  Construction of quantum codes from cyclic codes over Fp + vFp , 2015, Int. J. Inf. Coding Theory.

[20]  Mohammad Ashraf,et al.  Quantum codes from cyclic codes over F3 + vF3 , 2014 .

[21]  Manju Pruthi,et al.  The minimum Hamming distances of the irreducible cyclic codes of length , 2016 .

[22]  Wenping Ma,et al.  QUANTUM CODES FROM CYCLIC CODES OVER FINITE RING , 2009 .

[23]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.