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.
引用
收藏
页数：15
相关论文
共 50 条
  • [41] On the hulls of cyclic codes of oddly even length over Z4
    Pathak, Sachin
    Sharma, Anuradha
    DISCRETE MATHEMATICS, 2024, 347 (03)
  • [42] Infinite families of MDR cyclic codes over Z4 via constacyclic codes over Z4[u]/⟨u2-1⟩
    Han, Nayoung
    Kim, Bohyun
    Kim, Boran
    Lee, Yoonjin
    DISCRETE MATHEMATICS, 2020, 343 (03)
  • [43] Cyclic codes of odd length over Z4 [u] / ⟨uk⟩
    Cao, Yuan
    Li, Qingguo
    CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2017, 9 (05): : 599 - 624
  • [44] Cyclic codes of length 2e over Z4
    Abualrub, T
    Oehmke, R
    DISCRETE APPLIED MATHEMATICS, 2003, 128 (01) : 3 - 9
  • [45] On quasi-cyclic codes
    Heijnen, P
    van Tilborg, H
    Weijs, S
    1998 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 1998, : 65 - 65
  • [46] Shadow codes over Z4
    Dougherty, ST
    Harada, M
    Solé, P
    FINITE FIELDS AND THEIR APPLICATIONS, 2001, 7 (04) : 507 - 529
  • [47] Generalized Quasi-Cyclic Codes with Arbitrary Block Lengths
    Muchtadi-Alamsyah, Intan
    Irwansyah
    Barra, Aleams
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2022, 45 (03) : 1383 - 1407
  • [48] Generalized Quasi-Cyclic Codes with Arbitrary Block Lengths
    Intan Muchtadi-Alamsyah
    Aleams Irwansyah
    Bulletin of the Malaysian Mathematical Sciences Society, 2022, 45 : 1383 - 1407
  • [49] Cyclic codes over Z4 + uZ4 + u2Z4
    Ozen, Mehmet
    Ozzaim, Nazmiye Tugba
    Aydin, Nuh
    TURKISH JOURNAL OF MATHEMATICS, 2017, 41 (05) : 1235 - 1247
  • [50] Quasi-cyclic codes with cyclic constituent codes
    Lim, Chong Jie
    FINITE FIELDS AND THEIR APPLICATIONS, 2007, 13 (03) : 516 - 534
12345