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TitlePolycyclic codes over Galois rings with applications to repeated-root constacyclic codes
Author(s) Sergio R. López-Permouth, Steve Szabo, Hakan Özadam, Ferruh Özbudak
TypeArticle in Journal
AbstractCyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR ( p a , m ) and generating sets for its ideals are considered. It is shown that these generating sets are strong Groebner bases. A method for finding such sets in the case that a = 2 is given. This explicitly gives the Hamming distance of all cyclic codes of length p s over GR ( p 2 , m ) . The Hamming distance of certain constacyclic codes of length η p s over F p m is computed. A method, which determines the Hamming distance of the constacyclic codes of length η p s over GR ( p a , m ) , where ( η , p ) = 1 , is described. In particular, the Hamming distance of all cyclic codes of length p s over GR ( p 2 , m ) and all negacyclic codes of length 2 p s over F p m is determined explicitly.
KeywordsLinear codes, Cyclic codes, Constacyclic codes, Galois rings, Groebner basis, Repeated-root cyclic codes, Torsion codes
ISSN1071-5797
URL http://www.sciencedirect.com/science/article/pii/S1071579712000901
LanguageEnglish
JournalFinite Fields and Their Applications
Volume19
Number1
Pages16 - 38
Year2013
Edition0
Translation No
Refereed No
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