Details:
Title  1generator quasicyclic codes over finite chain rings.  Author(s)  Yonglin Cao  Type  Article in Journal  Abstract  Let R be an arbitrary commutative finite chain ring with 1≠0. 1generator quasicyclic (QC) codes over R are considered in this paper. Let γ be a fixed generator of the maximal ideal of R, F=R/⟨γ⟩ and F=q. For any positive integers m, n satisfying gcd(q,n)=1, let n=R[x]/⟨xn−1⟩. Then 1generator QC codes over R of length mn and index m can be regarded as 1generator nsubmodules of the module mn. First, we consider the parity check polynomial of a 1generator QC code and the properties of the code determined by the parity check polynomial. Then we give the enumeration of 1generator QC codes with a fixed parity check polynomial in standard form over R. Finally, under the condition that gcd(qn,m)=1, where qn denotes the order of q modulo n, we describe an algorithm to list all distinct 1generator quasicyclic codes with a fixed parity check polynomial in standard form over R of length mn and index m.  Keywords  Quasicyclic code, Finite chain ring, Parity check, polynomial in standard form, Gröbner basis, Direct sum, decomposition  ISSN  09381279; 14320622/e 
URL 
http://link.springer.com/article/10.1007%2Fs0020001201828 
Language  English  Journal  Appl. Algebra Eng. Commun. Comput.  Volume  24  Number  1  Pages  5372  Publisher  Springer, Berlin/Heidelberg  Year  2013  Edition  0  Translation 
No  Refereed 
No 
