Details:
Title | 1-generator quasi-cyclic 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. 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. | Keywords | | ISSN | 0938-1279; 1432-0622/e |
URL |
http://link.springer.com/article/10.1007%2Fs00200-012-0182-8 |
Language | English | Journal | Appl. Algebra Eng. Commun. Comput. | Volume | 24 | Number | 1 | Pages | 53--72 | Publisher | Springer, Berlin/Heidelberg | Year | 2013 | Edition | 0 | Translation |
No | Refereed |
No |
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