Abstract
Let M(n, d) be the maximum size of a permutation code of length n and distance d. In this note, the permutation codewords of a classical code C are considered. These are the codewords with all different entries in C. Using these codewords for Reed–Solomon codes, we present some good permutation codes in this class of codes. As a consequence, since these codes are subsets of Reed–Solomon codes, decoding algorithms known for Reed–Solomon codes can also be used as a decoding algorithm for them.
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Acknowledgements
The authors would like to thank anonymous referees whose comments greatly improved the results and presentation of the paper. The first author was supported in part by Grant No. 95050080 from School of Mathematics, Institute for Research in Fundamental Sciences (IPM). The second author was supported in part by Grant No. 96050219 from School of Mathematics, Institute for Research in Fundamental Sciences (IPM). The second author was additionally financially supported by the Center of Excellence for Mathematics at the University of Isfahan.
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Sobhani, R., Abdollahi, A., Bagherian, J. et al. A note on good permutation codes from Reed–Solomon codes. Des. Codes Cryptogr. 87, 2335–2340 (2019). https://doi.org/10.1007/s10623-019-00621-0
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DOI: https://doi.org/10.1007/s10623-019-00621-0