Further Results on the Existence of Splitting BIBDs and Application to Authentication Codes |
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Authors: | Jinhua Wang Renwang Su |
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Institution: | 1.School of Sciences,Nantong University,Nantong,People’s Republic of China;2.College of Statistics and Computing Science,Zhejiang Gongshang University,Hangzhou,People’s Republic of China |
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Abstract: | Let (v,u×c,λ)-splitting BIBD denote a (v,u×c,λ)-splitting balanced incomplete block design of order v with block size u×c and index λ. Necessary conditions for the existence of a (v,u×c,λ)-splitting BIBD are v≥uc, λ(v−1)≡0 (mod c(u−1)) and λ
v(v−1)≡0 (mod (c
2
u(u−1))). We show in this paper that the necessary conditions for the existence of a (v,3×3,λ)-splitting BIBD are also sufficient with possible exceptions when (1) (v,λ)∈{(55,1),(39,9k):k=1,2,…}, (2) λ≡0 (mod 54) and v≡0 (mod 2). We also show that there exists a (v,3×4,1)-splitting BIBD when v≡1 (mod 96). As its application, we obtain a new infinite class of optimal 4-splitting authentication codes. |
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Keywords: | |
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