On Generalized Quasi-Cyclic Codes over Finite Chain Rings

CUI Mengyao, GAO Jian, MA Fanghui, MENG Xiangrui

Journal of Systems Science and Mathematical Sciences ›› 2022, Vol. 42 ›› Issue (11) : 3134-3148.

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PDF(398 KB)
Journal of Systems Science and Mathematical Sciences ›› 2022, Vol. 42 ›› Issue (11) : 3134-3148. DOI: 10.12341/jssms22132

On Generalized Quasi-Cyclic Codes over Finite Chain Rings

  • CUI Mengyao, GAO Jian, MA Fanghui, MENG Xiangrui
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Abstract

Explicit generators of generalized quasi-cyclic (GQC) codes of general index over the finite chain ring are of great significance for determining the generator matrix, the duality, the enumeration, the minimum distance bound, the hull and the weight distribution of GQC codes. Let R=Fq+uFq++us1Fq, where q is a prime power, s is a positive integer, s2 and us=0. A GQC code of block lengths (r1,r2,,rl) with index l over R can be viewed as an R[x]-submodule of R[x]/xr11×R[x]/xr21××R[x]/xrl1. In this paper, we determine the generators and the minimum generating sets of GQC codes with general index over the finite chain ring R. We also determine the relationship of generators between GQC codes and their dual codes.

Key words

Generalized quasi-cyclic codes / generators / minimal generating sets / dual codes

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CUI Mengyao , GAO Jian , MA Fanghui , MENG Xiangrui. On Generalized Quasi-Cyclic Codes over Finite Chain Rings. Journal of Systems Science and Mathematical Sciences, 2022, 42(11): 3134-3148 https://doi.org/10.12341/jssms22132

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