On generalized quasi-cyclic codes over $\mathbb{Z}_4$
Jian Gao, Xiangrui Meng, Fang-Wei Fu
TL;DR
This paper investigates the algebraic structure of generalized quasi-cyclic codes over Z_4, providing new insights and constructions for Z_4-linear and nonlinear binary codes.
Contribution
It introduces new structural results for GQC codes over Z_4 and constructs novel Z_4-linear and nonlinear binary codes.
Findings
Derived normalized generating sets for GQC codes over Z_4
Established minimum generating sets and dual code structures
Constructed new Z_4-linear and nonlinear binary codes
Abstract
Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over including the normalized generating set, the minimum generating set and the normalized generating set of their dual codes. As an application, new -linear codes and good nonlinear binary codes are constructed from GQC codes over .
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Taxonomy
TopicsCoding theory and cryptography · Islamic Finance and Communication · Cancer Mechanisms and Therapy