Message authentication code (MAC) is one of the most fundamental cryptographic primitives, and aggregate message authentication code (AMAC) is an authentication technique that can compress multiple MAC tags into a short tag for messages from multiple senders. Although AMAC cannot specify an invalid message, AMAC with detecting functionality (AMAD) enables us to compress multiple MAC tags and to identify an invalid message. In this paper, we propose construction of AMAD from biorthogonal codes, and show that our AMAD achieves a better compression rate than other constructions of AMAD.