Dual generalizations of the concept of cyclicity of codes
Sergio R. López-Permouth, Benigno R. Parra-Avila, Steve Szabo · Advances in Mathematics of Communications · 2009
In this paper we focus on two generalizations of the notion ofcyclicity of codes: polycyclic codes and sequential codes. Weestablish a duality between these two generalizations and also showconnections between them and other well-known generalizations ofcyclicity such as the notions of negacyclicity and constacyclicity.In particular, it is shown that a code $C$ is sequential andpolycyclic if and only if $C$ and its dual C⊥ are bothsequential if and only if $C$ and its dual C⊥ are bothpolycyclic. Furthermore, any one of these equivalent statementscharacterizes the family of constacyclic codes.