Details:
Title  Polycyclic codes over Galois rings with applications to repeatedroot constacyclic codes  Author(s)  Sergio R. LópezPermouth, Steve Szabo, Hakan Özadam, Ferruh Özbudak  Type  Article in Journal  Abstract  Cyclic, 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.  Keywords  Linear codes, Cyclic codes, Constacyclic codes, Galois rings, Groebner basis, Repeatedroot cyclic codes, Torsion codes  ISSN  10715797 
URL 
http://www.sciencedirect.com/science/article/pii/S1071579712000901 
Language  English  Journal  Finite Fields and Their Applications  Volume  19  Number  1  Pages  16  38  Year  2013  Edition  0  Translation 
No  Refereed 
No 
