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Quasi-Cyclic Codes Over Finite Chain Rings

Information Theory 2013-09-09 v1 math.IT

Abstract

In this paper, we mainly consider quasi-cyclic (QC) codes over finite chain rings. We study module structures and trace representations of QC codes, which lead to some lower bounds on the minimum Hamming distance of QC codes. Moreover, we investigate the structural properties of 1-generator QC codes. Under some conditions, we 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.

Keywords

Cite

@article{arxiv.1309.1623,
  title  = {Quasi-Cyclic Codes Over Finite Chain Rings},
  author = {Jian Gao and Linzhi Shen and Fang-Wei Fu},
  journal= {arXiv preprint arXiv:1309.1623},
  year   = {2013}
}

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R2 v1 2026-06-22T01:22:06.561Z