A New Class of \(2\)-Fold Perfect 4\)-Splitting Authentication Codes

Abstract

Restricted strong partially balanced \(t\)-designs were first formulated by Pei, Li, Wang, and Safavi-Naini in their investigation of authentication codes with arbitration. We recently proved that optimal splitting authentication 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 balanced 2-designs, ORSPBD\((v, 2 \times 4, 1)\), and shows that there exists an ORSPBD\((v, 2 \times 4, 1)\) for even \(v\). As its application, we obtain a new infinite class of 2-fold perfect \(4\)-splitting authentication codes.