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Dual generalizations of the concept of cyclicity of codes

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  • 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.

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