New Infinite Class Of2-fold Perfect Splitting Authentication Codes

If a restricted partially balanced t-design RPBD(v,b,u×k;λ,0) is a restricted partially balanced s-design RPBD(v,b,u×k;λ,0) for0<s<t as well, then it is called a restricted strong partially balanced t-design and is denoted by t-design RSPBD(v,b,u×k;λ,0). Restricted strong partially balanced t-designs were first for-mulated by Pei, Li, Wang and Safavi-Naini [Characterization of authentication codes with arbitration. Lecture Notes in Computer Science.1587(1999). Springer-Verlag. Berlin-Heidelberg-New York. pp.303-313] investigation of authentication codes with arbitration. Liang and Du [A new class of3-fold perfect splitting authentication codes Des. Codes Cryptogr.,62(2012),109-119.] in recent proved that optimal splitting au-thentication codes that are multi-fold perfect against spoofing can be characterized in terms of restricted strong partially balanced t-designs. This article investigates the existence of optimal restricted strong partially balanced2-design ORSPBD(v,2×4,1), and shows that there exists an ORSPBD(v,2×4.1) for even v≥8. As its application. we obtain a new infinite class of2-fold perfect splitting authentication codes.