New High-Rate Self-Orthogonal Convolutional Codes with Small Distance

We list triangle difference sets that define self-orthogonal convolutional codes with relative code rate $R=k/(k+1)$, where $k$ is any positive integer and $d_{\min}=4,5,6$. For $d_{\min}=4$ , the constructed codes are either optimal or quasioptimal; for $d_{\min}=5$ and $k>11$, they are shorter than the best known codes by a factor of 1.8 to 2.5, and for $d_{\min}=6$ and $k\geq 8$ , they are shorter than the best known codes (for $k\geq 9$, by a factor of 1.5 to 1.8).