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August  2009, 3(3): 227-234. doi: 10.3934/amc.2009.3.227

Dual generalizations of the concept of cyclicity of codes

Sergio R. López-Permouth 1, , Benigno R. Parra-Avila 1, and  Steve Szabo 1,

1. 

Department of Mathematics, Ohio University, Athens, Ohio-45701, United States, United States, United States

Received  December 2008 Revised  May 2009 Published  August 2009

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.
Keywords: Cyclic codes, negacyclic codes., sequential codes, polycyclic codes, constacyclic codes.
Mathematics Subject Classification: Primary 94B15; Secondary 94B60, 94B0.
Citation: Sergio R. López-Permouth, Benigno R. Parra-Avila, Steve Szabo. Dual generalizations of the concept of cyclicity of codes. Advances in Mathematics of Communications, 2009, 3 (3) : 227-234. doi: 10.3934/amc.2009.3.227
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