Quasi-Cyclic Codes Over Finite Chain Rings

2013/09/06 by Jian Gao, Linzhi Shen, Gao, Jian +4 · 1 citation
Computer Science · Engineering · Mathematics · #11T71 #94B05 #94B15 #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT #msc:11T71 #msc:94B05 #msc:94B15

paper · pdf · doi:10.48550/arxiv.1309.1623

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arxiv created 2013/09/06 · openalex publication_date 2013/09/06 · arxiv updated 2013/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• One generator (1+u)-quasi twisted codes over F₂+uF₂

Cited by

• On cyclic codes over ℤ_q+uℤ_q

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