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Perfect difference families (PDFs for short) are important both intheoretical and in applications. Perfect difference matrices (PDMs for short)and the equivalent structure had been extensively studied and used to constructperfect difference families, radar array and related codes. The necessarycondition for the existence of a PDM$(n,m)$ is $m\equiv 1\pmod2$ and $m\geqn+1$. So far, PDM$(3,m)$s exist for odd $5\leq m\leq 201$ with two definiteexceptions of $m=9,11$. In this paper, new recursive constructions onPDM$(3,m)$s are investigated, and it is proved that there exist PDM$(3,m)$s forany odd $5\leq m<1000$ with two definite exceptions of $m=9,11$ and $33$possible exceptions. A complete result of $(g,\{3,4\},1)$-PDFs with the ratioof block size $4$ no less than $\frac{1}{14}$ is obtained. As an application, acomplete class of perfect strict optical orthogonal codes with weights $3$ and$4$ is obtained.

Constructions and Applications of Perfect Difference Matrices and Perfect Difference Families