Abstract
Authentication codes with arbitration protect against deceptions from the transmitter and the receiver as well as that from the opponent. An authentication code with arbitration is t-fold perfect if the numbers of decoding rules and encoding rules meet the information-theoretic lower bounds. Pei (Message authentication codes (in Chinese). USCT, Hefei, 2009) pointed out that there has not yet been able to construct t-fold perfect authentication codes with arbitration for \(t > 2\). In this paper, we define a new design, perfect strong strict restricted partially balanced t-design, and prove that the existence of perfect strong strict restricted partially balanced t-designs implies the existence of t-fold perfect authentication codes with arbitration. Further, we obtain some new infinite classes of t-fold perfect authentication codes with arbitration.
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This work was supported by the National Natural Science Foundation of China (Grant No. 11171248).
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Communicated by C. J. Colbourn.
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Liang, M., Li, M. & Du, B. A construction for t-fold perfect authentication codes with arbitration. Des. Codes Cryptogr. 73, 781–790 (2014). https://doi.org/10.1007/s10623-013-9826-3
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DOI: https://doi.org/10.1007/s10623-013-9826-3
Keywords
- t-Fold perfect authentication code with arbitration
- Perfect strong strict restricted partially balanced t-design