Abstract
Optimal restricted strong partially balanced t-design can be used to construct splitting authentication codes which achieve combinatorial lower bounds or information-theoretic lower bounds. In this paper, we investigate the existence of optimal restricted strong partially balanced 2-designs ORSPBD (v, k×c,1), and show that there exists an ORSPBD (v,2×c,1) for any positive integer v≡ v 0 (mod 2c 2) and \(v_{0}\in \{1\leq x\leq 2c^{2}:\ \gcd (x,c)=1\ \text {or} \ \gcd (x,c)=c \} \setminus \) \(\{c^{2}+1\leq x\leq (c+1)^{2} :\gcd (x,c)=1\ \text {and}\ \gcd (x,2)=2\}\). Furthermore, we determine the existence of an ORSPBD (v,k×c,1) for any integer v≥k c with (k,c)=(2,4), (2,5), (3,2) or for any even integer v≥k c with (k,c)=(4,2). As their applications, we obtain six new infinite classes of 2-fold optimal or perfect c-splitting authentication codes.
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The authors would like to express their heartfelt gratitude to Professor B. Du for his many constructive discussions and suggestions.
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Miao Liang is supported by NSFC Grants 11301370, 11571251 and sponsored by Qing Lan Project. Lijun Ji is supported by NSFC Grants 11222113, 11431003 and a project funded by the priority academic grogram development of JiangSu higher education institutions.
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Liang, M., Ji, L. & Zhang, J. Some new classes of 2-fold optimal or perfect splitting authentication codes. Cryptogr. Commun. 9, 407–430 (2017). https://doi.org/10.1007/s12095-015-0179-9
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DOI: https://doi.org/10.1007/s12095-015-0179-9