In this paper we focus on two generalizations of the notion of
cyclicity of codes: polycyclic codes and sequential codes. We
establish a duality between these two generalizations and also show
connections between them and other well-known generalizations of
cyclicity such as the notions of negacyclicity and constacyclicity.
In particular, it is shown that a code $C$ is sequential and
polycyclic if and only if $C$ and its dual C⊥ are both
sequential if and only if $C$ and its dual C⊥ are both
polycyclic. Furthermore, any one of these equivalent statements
characterizes the family of constacyclic codes.
Mathematics Subject Classification: Primary 94B15; Secondary 94B60, 94B05.