A class of 1-generator quasi-cyclic codes over finite chain rings |
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Authors: | Jian Gao Linzhi Shen |
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Affiliation: | Chern Institute of Mathematics and LPMC, Nankai University, 300071, Tianjin, China |
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Abstract: | Using another method, which is different with the one given by Cao [1-generator quasi-cyclic (QC) codes over finite chain rings, Appl. Algebra Eng. Commun. Comput. 24 (2013), pp. 53–72], we investigate the structural properties of a class of 1-generator QC codes over finite chain rings. We give the structure of the annihilator of 1-generator QC codes, the conditions for 1-generator QC codes to be free and the minimum distance bounds on 1-generator QC codes. Under some conditions, we also discuss the enumeration of 1-generator QC codes and describe how to obtain the one and only one generator for each 1-generator QC code. |
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Keywords: | finite chain rings 1-generator quasi-cyclic codes minimum distance enumeration generator |
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