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On the Existence of Splitting Balanced Incomplete Block Designs

WANG Jin-hua,GAO Hua,WANG Xin(School of Sciences,Nantong University,Nantong 226007,China)  
Let(v,u×c,λ)-SBIBD denote a(v,u×c,λ)-splitting balanced incomplete block design of order with block size and index.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 λv(v-1)≡0(mod c2u(u-1)).The investigation for the existence of splitting BIBDs has theoretical sig-nificance and is closely connected with design theory,graph theory and splitting authentication codes.In this paper,applying difference method and recursive construction,we show that there exists a(v,3 × 4,1)-splitting balanced in-complete block design for v≡1(mod 96).As its consequence,we obtain a new infinite class of optimal 4-splitting au-thentication codes.
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