Output symbols are generated using input symbols and basis elements. A plurality of basis elements are generated. Each basis element is generated from a predetermined function of associated input symbols associated with the basis element. For each output symbol, a set of associated basis elements associated with the output symbol is determined, and a set of direct associated input symbols directly associated with the output symbol is determined. For each output symbol, the output symbol is generated from a predetermined function of the associated basis elements and the associated input symbols.