A construction for t-fold perfect authentication codes with arbitration |
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Authors: | Miao Liang Mingchao Li Beiliang Du |
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Institution: | 1. Foundation Department, Suzhou Vocational University, Suzhou, 215104, People’s Republic of China 3. Department of Mathematics, Soochow University (Suzhou University), Suzhou, 215006, People’s Republic of China 2. College of Science, Hebei University of Engineering, Handan, 056038, People’s Republic of China
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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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