Des. Codes Cryptogr. (2011) 61:1–9 DOI 10.1007/s10623-010-9435-3 Decoding permutation arrays with ternary vectors Chia-Jung Lee · Te-Tsung Lin · Min-Zheng Shieh · Shi-Chun Tsai · Hsin-Lung Wu Received: 29 December 2008 / Revised: 9 September 2010 / Accepted: 15 September 2010 / Published online: 5 October 2010 © Springer Science+Business Media, LLC 2010 Abstract We give an explicit decoding scheme for the permutation arrays under Hamming distance metric, where the encoding is constructed via a distance-preserving mapping from ternary vectors to permutations (3-DPM). Keywords Permutation array · Ternary code · Decoding · Hamming distance Mathematics Subject Classification (2000) 94B05 · 94B25 Communicated by P. Wild. C.-J. Lee · T.-T. Lin · M.-Z. Shieh · S.-C. Tsai (B ) · H.-L. Wu Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan e-mail: sctsai@csie.nctu.edu.tw C.-J. Lee e-mail: leecj@iis.sinica.edu.tw T.-T. Lin e-mail: atman.cs94g@nctu.edu.tw M.-Z. Shieh e-mail: mzhsieh@csie.nctu.edu.tw H.-L. Wu e-mail: hsinlung@mail.ntpu.edu.tw Present Address: C.-J. Lee Institute of Information Science, Academia Sinica, Taipei 11529, Taiwan Present Address: H.-L. Wu Department of Computer Science and Information Engineering, National Taipei University, Taipei 237, Taiwan 123