  Group network codes are a generalization of linear codes that have seen
several studies over the last decade. When studying network codes, operations
performed at internal network nodes called local encoding functions, are of
significant interest. While local encoding functions of linear codes are well
understood (and of operational significance), no similar operational definition
exists for group network codes. To bridge this gap, we study the connections
between group network codes and a family of codes called Coordinate-Wise-Linear
(CWL) codes. CWL codes generalize linear codes and, in addition, can be defined
locally (i.e., operationally). In this work, we study the connection between
CWL codes and group codes from both a local and global encoding perspective. We
show that Abelian group codes can be expressed as CWL codes and, as a result,
they inherit an operational definition.
