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Title1-generator quasi-cyclic codes over finite chain rings.
Author(s) Yonglin Cao
TypeArticle in Journal
AbstractLet R be an arbitrary commutative finite chain ring with 1≠0. 1-generator quasi-cyclic (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 1-generator QC codes over R of length mn and index m can be regarded as 1-generator n-submodules of the module mn. First, we consider the parity check polynomial of a 1-generator QC code and the properties of the code determined by the parity check polynomial. Then we give the enumeration of 1-generator QC codes with a fixed parity check polynomial in standard form over R. Finally, under the condition that gcd(|q|n,m)=1, where |q|n denotes the order of q modulo n, we describe an algorithm to list all distinct 1-generator quasi-cyclic codes with a fixed parity check polynomial in standard form over R of length mn and index m.
KeywordsQuasi-cyclic code, Finite chain ring, Parity check, polynomial in standard form, Gröbner basis, Direct sum, decomposition
ISSN0938-1279; 1432-0622/e
URL http://link.springer.com/article/10.1007%2Fs00200-012-0182-8
JournalAppl. Algebra Eng. Commun. Comput.
PublisherSpringer, Berlin/Heidelberg
Translation No
Refereed No