FIVE-LEE-WEIGHT LINEAR CODES OVER F q + u F q

被引：0
|
作者：
Kumar, Payan [1 ,2 ]
Khan, Noor mohammad [1 ]
机构：
[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, India
[2] Indian Inst Sci, Dept Elect Syst Engn, Bengaluru 560012, India
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2025年
关键词：
Linear code; Gauss sum; Weight distribution; Complete weight enu- merator; Secret sharing scheme; COMPLETE WEIGHT ENUMERATORS; 3-WEIGHT CODES; CONSTRUCTION;
D O I：
10.3934/amc.2025002
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this study, linear codes having their Lee-weight distributions over the semi-local ring F q + uF q with u 2 = 1 are constructed using the defining set and Gauss sums for an odd prime q. Moreover, we derive complete Hamming-weight enumerators for the images of the constructed linear codes under the Gray map. We finally show an application to secret sharing schemes.
引用
收藏
页数：16
相关论文
共 50 条
  • [31] Type 2 constacyclic codes over F2m[u]/⟨u3⟩ of oddly even length
    Cao, Yuan
    Cao, Yonglin
    Dinh, Hai Q.
    Fu, Fang-Wei
    Gao, Yun
    Sriboonchitta, Songsak
    DISCRETE MATHEMATICS, 2019, 342 (02) : 412 - 426
  • [32] Macwilliams identities of linear codes over the ring F 2 + uF 2 + vF2
    Liu Xiusheng
    Liu Hualu
    JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2015, 28 (03) : 691 - 701
  • [33] Some results on the linear codes over the finite ring F2 + v1F2 + ... + vrF2
    Dertli, Abdullah
    Cengellenmis, Yasemin
    Eren, Senol
    INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2016, 14 (01)
  • [34] Complete weight enumerators of linear codes over non-principal idea ring
    Xu, Heqian
    Du, Wei
    Journal of Computational Information Systems, 2014, 10 (15): : 6435 - 6442
  • [35] On codes over Fq+vFq+v2Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{q}+v\mathbb {F}_{q}+v^{2}\mathbb {F}_{q}$$\end{document}
    A. Melakhessou
    K. Guenda
    T. A. Gulliver
    M. Shi
    P. Solé
    Journal of Applied Mathematics and Computing, 2018, 57 : 375 - 391
  • [36] Construction of one-gray weight codes and two-Gray weight codes over ℤ4 + uℤ4
    Minjia Shi
    Dandan Wang
    Jian Gao
    Bo Wu
    Journal of Systems Science and Complexity, 2016, 29 : 1472 - 1484
  • [37] Skew cyclic codes over F4R
    Benbelkacem, Nasreddine
    Ezerman, Martianus Frederic
    Abualrub, Taher
    Aydin, Nuh
    Batoul, Aicha
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022, 21 (04)
  • [38] Lee-extremal self-dual codes over F2 + uF2 of lengths 23 and 24
    Kim, Hyun Jin
    FINITE FIELDS AND THEIR APPLICATIONS, 2014, 29 : 18 - 33
  • [39] Complete classification of (δ plus αu2)-constacyclic codes over F2m[u]/⟨u4⟩ of oddly even length
    Cao, Yuan
    Cao, Yonglin
    Ma, Fanghui
    DISCRETE MATHEMATICS, 2017, 340 (12) : 2840 - 2852
  • [40] The weight distributions of linear sets in PG(1, q5)
    De Boeck, Maarten
    Van de Voorde, Geertrui
    FINITE FIELDS AND THEIR APPLICATIONS, 2022, 82
12345