[1]
|
A. Barg and A. Mazumdar, Codes in permutations and error correction for rank modulation, IEEE Trans. Inf. Theory, 56 (2010), 3158-3165.
doi: 10.1109/TIT.2010.2048455.
|
[2]
|
I. F. Blake, Permutation codes for discrete channels (Corresp.), IEEE Trans. Inform. Theory, 20 (1974), 138-140.
doi: 10.1109/TIT.1974.1055142.
|
[3]
|
I. F. Blake, Coding with permutations, Information and Control, 43 (1979), 1-19.
doi: 10.1016/S0019-9958(79)90076-7.
|
[4]
|
S. Buzaglo and T. Etzion, Bounds on the size of permutation codes with the Kendall $\tau$-metric, IEEE Trans. Inf. Theory, 61 (2015), 3241-3250.
doi: 10.1109/TIT.2015.2424701.
|
[5]
|
W. Chu, C. J. Colbourn and P. Dukes, Constructions for permutation codes in powerline communications, Des. Codes Cryptogr., 32 (2004), 51-64.
doi: 10.1023/B:DESI.0000029212.52214.71.
|
[6]
|
C. J. Colbourn, T. Kløve and A. C. H. Ling, Permutation arrays for powerline communication and mutually orthogonal Latin squares, IEEE Trans. Inform. Theory, 50 (2004), 1289-1291.
doi: 10.1109/TIT.2004.828150.
|
[7]
|
D. R. de la Torre, C. J. Colbourn and A. C. H. Ling, An application of permutation arrays to block ciphers, Congr. Numer., 145 (2000), 5-7.
|
[8]
|
M. Deza and H. Huang, Metrics on permutations, a survey, J. Combinat. Inf. Syst. Sci., 23 (1998), 173-185.
|
[9]
|
M. Deza and S. A. Vanstone, Bounds for permutation arrays, J. Statist. Plann. Inference, 2 (1978), 197-209.
doi: 10.1016/0378-3758(78)90008-3.
|
[10]
|
C. Ding, F-W. Fu, T. Kløve and V. K.-W. Wei, Constructions of permutation arrays, IEEE Trans. Inf. Theory, 48 (2002), 977-980.
doi: 10.1109/18.992812.
|
[11]
|
P. Dukes and N. Sawchuck, Bounds on permutation codes of distance four, J. Algebraic Combin., 31 (2010), 143-158.
doi: 10.1007/s10801-009-0191-2.
|
[12]
|
F. Farnoud, V. Skachek and O. Milenkovic, Error-Correction in flash memories via codes in the Ulam metric, IEEE Trans. Inf. Theory, 59 (2013), 3003-3020.
doi: 10.1109/TIT.2013.2239700.
|
[13]
|
P. Frankl and M. Deza, On the maximum number of permutations with given maximal or minimal distance, J. Combinatorial Theory, Series A, 22 (1977), 352-360.
doi: 10.1016/0097-3165(77)90009-7.
|
[14]
|
F.-W. Fu and T. Kløve, Two constructions of permutations arrays, IEEE Trans. Inform. Theory, 50 (2004), 881-883.
doi: 10.1109/TIT.2004.826659.
|
[15]
|
F. Gao, Y. Yang and G. N. Ge, An improvement on the Gilbert-Varshamov bound for permutation codes, IEEE Trans. Inform. Theory, 59 (2013), 3059-3063.
doi: 10.1109/TIT.2013.2237945.
|
[16]
|
A. Jiang, M. Schwartz and J. Bruck, Error-correcting codes for rank modulation, Proc. IEEE Int. Symp. Information Theory, (2008), 6-11.
doi: 10.1109/ISIT.2008.4595285.
|
[17]
|
A. Jiang, M. Schwartz and J. Bruck, Correcting charge-constrained errors in the rank-modulation scheme, IEEE Trans. Inf. Theory, 56 (2010), 2112-2120.
doi: 10.1109/TIT.2010.2043764.
|
[18]
|
T. Kløve, T. T. Lin, S. C. Tsai and W. G. Tzeng, Permutation arrays under the Chebyshev distance, IEEE Trans. Inf. Theory, 56 (2010), 2611-2617.
doi: 10.1109/TIT.2010.2046212.
|
[19]
|
J. Kong and M. Hagiwara, Nonexistence of perfect permutation codes in the Ulam metric, Proc. IEEE Int. Symp. Inf. Theory and its Applications, (2016), 691-695.
|
[20]
|
R. Montemanni and D. H. Smith, A new table of permutation codes, Des. Codes Cryptogr., 63 (2012), 241-253.
doi: 10.1007/s10623-011-9551-8.
|
[21]
|
N. Pavlidou, A. J. H. Vinck, J. Yazdani and B. Honary, Power line communications: State of the art and future trends, IEEE Communications Magazine, 41 (2003), 34-40.
doi: 10.1109/MCOM.2003.1193972.
|
[22]
|
M. Tait, A. Vardy and J. Verstraete, Asymptotic improvement of the Gilbert-Varshamov bound on the size of permutation codes, preprint, arXiv: 1311.4925, 2013.
|
[23]
|
H. Tarnanen, Upper bounds on permutation codes via linear programming, European J. Combin., 20 (1999), 101-114.
doi: 10.1006/eujc.1998.0272.
|
[24]
|
A. J. H. Vinck, Coded modulation for power line communications, In AE Int. J. Electron. and Commun, (2011), 45-49.
|
[25]
|
X. Wang and F.-W. Fu, On the snake-in-the-box codes for rank modulation under Kendall's $\tau$-metric, Des. Codes Cryptogr., 83 (2017), 455-465.
doi: 10.1007/s10623-016-0239-y.
|
[26]
|
X. Wang and F.-W. Fu, Snake-in-the-box codes under the $\ell_{\infty}$-metric for rank modulation, Des. Codes Cryptogr., 88 (2020), 487-503.
doi: 10.1007/s10623-019-00693-y.
|
[27]
|
X. Wang, Y. J. Wang, W. J. Yin and F-W. Fu, Nonexistence of perfect permutation codes under the Kendall $\tau$-metric, Des. Codes Cryptogr., 89 (2021), 2511-2531.
doi: 10.1007/s10623-021-00934-z.
|
[28]
|
X. Wang, Y. W. Zhang, Y. T. Yang and G. N. Ge, New bounds of permutation codes under Hamming metric and Kendall's $\tau$-metric, Des. Codes Cryptogr., 85 (2017), 533-545.
doi: 10.1007/s10623-016-0321-5.
|
[29]
|
Y. Yehezkeally and M. Schwartz, Snake-in-the-box codes for rank modulation, IEEE Trans. Inf. Theory, 58 (2012), 5471-5483.
doi: 10.1109/TIT.2012.2196755.
|
[30]
|
Y. W. Zhang and G. N. Ge, Snake-in-the-box codes for rank modulation under Kendall's $\tau$-metric, IEEE Trans. Inf. Theory, 62 (2016), 151-158.
doi: 10.1109/TIT.2015.2502602.
|