On generalized quasi-cyclic codes over Z4

被引：0
作者：
Meng, Xiangrui [1 ]
Gao, Jian [1 ]
Fu, Fang-Wei [2 ,3 ]
机构：
[1] Shandong Univ Technol, Sch Math & Stat, Zibo 255091, Peoples R China
[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China
[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
来源：
DISCRETE MATHEMATICS | 2024年 / 347卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Generalized quasi-cyclic codes; Normalized generating sets; Minimal generating sets; STRUCTURAL-PROPERTIES; Z(4);
D O I：
10.1016/j.disc.2023.113821
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important roles in coding theory. In this paper, we study some results on GQC codes over Z4 including normalized generating sets, minimal generating sets and normalized generating sets of their dual codes. As an application, new Z4-linear codes and good binary nonlinear codes are constructed from GQC codes over Z4. (c) 2023 Elsevier B.V. All rights reserved.
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页数：15
相关论文
共 25 条
[1]  
Asamov T., 2021, Table of Z4 codes.
[2]   Quasi-cyclic codes over Z4 and some new binary codes [J].
Aydin, N ;
Ray-Chaudhuri, DK .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (07) :2065-2069
[3]  
Aydin N., 2023, C2SI 2023, V13874, P395
[4]   A generalization of quasi-twisted codes: Multi-twisted codes [J].
Aydin, Nuh ;
Halilovic, Ajdin .
FINITE FIELDS AND THEIR APPLICATIONS, 2017, 45 :96-106
[5]   On normalized generating sets for GQC codes over Z2 [J].
Bae, Sunghan ;
Kang, Pyung-Lyun ;
Li, Chengju .
FINITE FIELDS AND THEIR APPLICATIONS, 2017, 45 :285-300
[6]  
Borges J, 2018, DESIGN CODE CRYPTOGR, V86, P463, DOI 10.1007/s10623-017-0334-8
[7]   The Magma algebra system .1. The user language [J].
Bosma, W ;
Cannon, J ;
Playoust, C .
JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265
[8]   Generalized quasi-cyclic codes over Galois rings: structural properties and enumeration [J].
Cao, Yonglin .
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2011, 22 (03) :219-233
[9]  
Dougherty ST, 2006, DESIGN CODE CRYPTOGR, V39, P127, DOI 10.1007/s10623-005-2773-x
[10]   Generalized quasi-cyclic codes: structural properties and code construction [J].
Esmaeili, M. ;
Yari, S. .
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2009, 20 (02) :159-173
123