A new class of 3-fold perfect splitting authentication codes

Restricted strong partially balanced t-designs were first formulated by Pei, Li, Wang and Safavi-Naini in investigation of authentication codes with arbitration. In this article, we will prove that splitting authentication codes that are multi-fold perfect against spoofing can be characterized in terms of restricted strong partially balanced t-designs. We will also investigate the existence of restricted strong partially balanced 3-designs RSPBD 3-(v, b, 3 × 2; ?1, ?2, 1, 0)s, and show that there exists an RSPBD 3-(v, b, 3 × 2; ?1, ?2, 1, 0) for any $${v\equiv 9\ (\mbox{{\rm mod}}\ 16)}$$ . As its application, we obtain a new infinite class of 3-fold perfect splitting authentication codes.