Perfect difference families (PDFs for short) are important both in theoretical and in applications. Perfect difference matrices (PDMs for short) and the equivalent structure had been extensively studied and used to construct perfect difference families, radar array and related codes. The necessary condition for the existence of a PDM$(n,m)$ is $m\equiv 1\pmod2$ and $m\geq n+1$. So far, PDM$(3,m)$s exist for odd $5\leq m\leq 201$ with two definite exceptions of $m=9,11$. In this paper, new recursive constructions on PDM$(3,m)$s are investigated, and it is proved that there exist PDM$(3,m)$s for any 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 ratio of block size $4$ no less than $\frac{1}{14}$ is obtained. As an application, a complete class of perfect strict optical orthogonal codes with weights $3$ and $4$ is obtained.

翻译：在理论和应用中,完全差异家庭(短差家庭)在理论和应用中都很重要。完美的差异矩阵(短差家庭)和同等结构已经进行了广泛的研究,并用于构建完美的差异家庭、雷达阵列和相关代码。存在一个PDM$(n,m)的必要条件是$m\equiv 1\pmod2美元和$m\geq n+1美元。到目前为止,奇数5美元(leq mleq mleq) 201美元的PDM$(3,m)美元存在,但两个明确的例外为9,11美元。在本文件中,对PDM$(3,m)的新循环建筑进行了调查,并证明存在5\leqm <1,000美元的PDM$(3,m)美元的任何奇数(5\leqm美元=9,11美元和3美元可能的例外。完整的结果为$(g,3,4 ⁇,1美元)-PDFFS,其区块面积比例不少于4美元=9,11美元。在本文中,新的PDM$(3+14美元)标准是完全的,是完全的,完全的。