Classification of binary self-orthogonal codes of lengths from 16 to 20 and its application

Kim and Ohk (2022) showed that binary self-orthogonal [n, k] codes for various dimensions k can be useful for the construction of DNA codes based on quasi self-dual codes over a noncommutative nonunital ring E with four elements. However, there is few classification of binary self-orthogonal codes with dimension ≥6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ge 6$$\end{document}. In this paper, we complete the classification of binary self-orthogonal codes of lengths from 16 to 20 with dimension ≥6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ge 6$$\end{document}. Hence, our classification extends a result of Kim and Ohk (2022).