Convolutional codes: techniques of construction

In this paper, we show how to construct new convolutional codes from old ones by applying the well-known techniques: puncturing, extending, expanding, direct sum, the (u|u+v)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathbf{u}| \mathbf{u}+\mathbf{v})$$\end{document} construction and the product code construction. By applying these methods, several new families of convolutional codes can be constructed. As an example of code expansion, families of convolutional codes derived from classical Bose–Chaudhuri–Hocquenghem, character codes and Melas codes are constructed.