On the Hamming weight of repeated root cyclic and negacyclic codes over Galois rings

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November 2009, 3(4): 409-420. doi: 10.3934/amc.2009.3.409

On the Hamming weight of repeated root cyclic and negacyclic codes over Galois rings

Sergio R. López-Permouth ^1, and Steve Szabo ^1,

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

Received July 2009 Revised September 2009 Published November 2009

Abstract
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Repeated root Cyclic and Negacyclic codes over Galois rings have been studied much less than their simple root counterparts. This situation is beginning to change. For example, repeated root codes of length p^s, where $p$ is the characteristic of the alphabet ring, have been studied under some additional hypotheses. In each one of those cases, the ambient space for the codes has turned out to be a chain ring. In this paper, all remaining cases of cyclic and negacyclic codes of length p^s over a Galois ring alphabet are considered. In these cases the ambient space is a local ring with simple socle but not a chain ring. Nonetheless, by reducing the problem to one dealing with uniserial subambients, a method for computing the Hamming distance of these codes is provided.

Keywords: Galois rings., Cyclic codes, negacyclic codes.

Mathematics Subject Classification: Primary 94B15; Secondary 94B60, 94B0.

Citation: Sergio R. López-Permouth, Steve Szabo. On the Hamming weight of repeated root cyclic and negacyclic codes over Galois rings. Advances in Mathematics of Communications, 2009, 3 (4) : 409-420. doi: 10.3934/amc.2009.3.409

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