Weight distributions of generalized quasi-cyclic codes over Fq plus uFq

被引：4
作者：
Gao, Jian [1 ]
Meng, Xiangrui [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：
FINITE FIELDS AND THEIR APPLICATIONS | 2023年 / 88卷
基金：
中国国家自然科学基金;
关键词：
Generalized quasi-cyclic codes; Weight distributions; Minimal linear codes; Projective two-weight codes; MINIMAL LINEAR CODES; CONSTRUCTION; 2-WEIGHT; SETS;
D O I：
10.1016/j.ffa.2023.102181
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, by Gauss sums, we determine Hamming weight distributions of generalized quasi-cyclic (GQC) codes over the finite chain ring Fq+uFq, where u2 = 0. As applications, some new infinite families of minimal linear codes with Wmin Wmax <= q-1 q and projective two-weight codes are constructed.(c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页数：42
相关论文
共 50 条
  • [1] Minimal vectors in linear codes
    Ashikhmin, A
    Barg, A
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (05) : 2010 - 2017
  • [2] On normalized generating sets for GQC codes over Z2
    Bae, Sunghan
    Kang, Pyung-Lyun
    Li, Chengju
    [J]. FINITE FIELDS AND THEIR APPLICATIONS, 2017, 45 : 285 - 300
  • [3] Minimal Linear Codes in Odd Characteristic
    Bartoli, Daniele
    Bonini, Matteo
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2019, 65 (07) : 4152 - 4155
  • [4] Cyclic codes and self-dual codes over F2+uF2
    Bonnecaze, A
    Udaya, P
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (04) : 1250 - 1255
  • [5] The Magma algebra system .1. The user language
    Bosma, W
    Cannon, J
    Playoust, C
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) : 235 - 265
  • [6] THE GEOMETRY OF 2-WEIGHT CODES
    CALDERBANK, R
    KANTOR, WM
    [J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1986, 18 : 97 - 122
  • [7] Structural properties and enumeration of 1-generator generalized quasi-cyclic codes
    Cao, Yonglin
    [J]. DESIGNS CODES AND CRYPTOGRAPHY, 2011, 60 (01) : 67 - 79
  • [8] Linear codes from simplicial complexes
    Chang, Seunghwan
    Hyun, Jong Yoon
    [J]. DESIGNS CODES AND CRYPTOGRAPHY, 2018, 86 (10) : 2167 - 2181
  • [9] Hamming weight distributions of multi-twisted codes over finite fields
    Chauhan, Varsha
    Sharma, Anuradha
    Sharma, Sandeep
    Yadav, Monika
    [J]. DESIGNS CODES AND CRYPTOGRAPHY, 2021, 89 (08) : 1787 - 1837
  • [10] Cohen Gerard D., 2013, Cryptography and Coding. 14th IMA International Conference, IMACC 2013. Proceedings: LNCS 8308, P85, DOI 10.1007/978-3-642-45239-0_6
12345