On the linear codes over the ring Rp

Some results are generalized on linear codes over Z3[v]/〈v3 − v〉 in [15] to the ring Rp = Zp[v]/〈vp − v〉, where p is an odd prime number. The Gray images of cyclic and quasi-cyclic codes over Rp ar...

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

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

[3]  Irfan Siap,et al.  Quantum codes from cyclic codes over a class of nonchain rings , 2015, 2015 6th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO).

[4]  Ali Ghrayeb,et al.  On the Construction of Skew Quasi-Cyclic Codes , 2008, IEEE Transactions on Information Theory.

[5]  Taher Abualrub,et al.  On θ-cyclic codes over F2 + vF2 , 2012 .

[6]  Patrick Solé,et al.  On the algebraic structure of quasi-cyclic codes III: generator theory , 2005, IEEE Transactions on Information Theory.

[7]  Irfan Siap,et al.  Structure of codes over the ring Z3[v]/(v3-v) , 2013, Appl. Algebra Eng. Commun. Comput..

[8]  Steven T. Dougherty,et al.  Codes over an infinite family of rings with a Gray map , 2014, Des. Codes Cryptogr..

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

[10]  Maheshanand Bhaintwal,et al.  On quasi-cyclic codes over $${\mathbb{Z}_q}$$ , 2009, Applicable Algebra in Engineering, Communication and Computing.

[11]  Wenping Ma,et al.  Gray Map and Quantum Codes over the Ring F_2+uF_2+u^2F_2 , 2011, 2011IEEE 10th International Conference on Trust, Security and Privacy in Computing and Communications.

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

[13]  Jian Gao,et al.  Skew Generalized Quasi-Cyclic Codes over Finite Fields , 2013, ArXiv.

[14]  A. Dertli,et al.  On the Codes over a Semilocal Finite Ring , 2015 .

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

[16]  Patrick Solé,et al.  Skew constacyclic codes over Galois rings , 2008, Adv. Math. Commun..

[17]  N. Sloane,et al.  Quantum error correction via codes over GF(4) , 1996, Proceedings of IEEE International Symposium on Information Theory.

[18]  Felix Ulmer,et al.  Skew-cyclic codes , 2006, Applicable Algebra in Engineering, Communication and Computing.

[19]  N. J. A. Sloane,et al.  The Z4-linearity of Kerdock, Preparata, Goethals, and related codes , 1994, IEEE Trans. Inf. Theory.

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

[21]  I. Siap,et al.  Cyclic and constacyclic codes over a non-chain ring , 2014 .

[22]  Maheshanand Bhaintwal.  Skew quasi-cyclic codes over Galois rings , 2012, Des. Codes Cryptogr..

[23]  Felix Ulmer,et al.  Coding with skew polynomial rings , 2009, J. Symb. Comput..

[24]  Shixin Zhu,et al.  (1+u) constacyclic and cyclic codes over F2+uF2 , 2006, Appl. Math. Lett..

[25]  Patanee Udomkavanich,et al.  Skew constacyclic codes over finite chain rings , 2010, Adv. Math. Commun..

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

[27]  Maheshanand Bhaintwal,et al.  On Quasi-cyclic Codes over Integer Residue Rings , 2007, AAECC.

[28]  Patrick Solé,et al.  On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings , 2003, Des. Codes Cryptogr..

[29]  Jian Gao.  SKEW CYCLIC CODES OVER Fp+ vFp , 2013 .

[30]  Mingzhong Wu.  Skew Cyclic and Quasi-Cyclic Codes of Arbitrary Length over Galois Rings , 2013 .

[31]  Quantum codes over the ring F_2 + uF_2 + u^2F_2 + ... + u^mF_2 , 2015 .

[32]  Shixin Zhu,et al.  A class of constacyclic codes over Fp+vFp and its Gray image , 2011, Discret. Math..

[33]  Irfan Siap,et al.  Structure of codes over the ring $$Z_{3}[v]/\langle v^{3}-v\rangle $$Z3[v]/〈v3−v〉 , 2013, Applicable Algebra in Engineering, Communication and Computing.

[34]  Patrick Solé,et al.  On the algebraic structure of quasi-cyclic codes I: Finite fields , 2001, IEEE Trans. Inf. Theory.

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

[36]  Jian Gao,et al.  Some results on linear codes over $$\mathbb {F}_p+u\mathbb {F}_p+u^2\mathbb {F}_p$$Fp+uFp+u2Fp , 2015 .

[37]  Taher Abualrub,et al.  Skew cyclic codes of arbitrary length , 2011, Int. J. Inf. Coding Theory.