Minimal linear codes from defining sets over Fp plus uFp

被引：1
|
作者：
Gao, Jian [1 ]
Zhang, Yaozong [1 ]
Meng, Xiangrui [2 ,3 ]
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, Anguilla
[3] Nankai Univ, Tianjin Key Lab Network & Data Secur Technol, LPMC, Tianjin 300071, Peoples R China
来源：
DISCRETE MATHEMATICS | 2023年 / 346卷 / 10期
基金：
中国国家自然科学基金;
关键词：
Linear codes; Exponential sums; Lee-weight distributions; Complete weight enumerator; Minimal linear codes; COMPLETE WEIGHT ENUMERATORS; FINITE-FIELDS; CYCLIC CODES; 3-WEIGHT; 2-WEIGHT; CONSTRUCTION; FAMILIES;
D O I：
10.1016/j.disc.2023.113584
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Minimal codes are a special type of linear codes, which have nice applications in secret sharing and secure two-party computation. How to construct new infinite family of minimal codes has been a hot topic in coding theory and cryptography. In this paper, by employing exponential sums, we study the Lee-weight distributions of several classes of linear codes from defining sets over the finite chain ring Fp + uFp and determine exactly the complete weight enumerator of their Gray images under the Gray map. Furthermore, we prove that the Gray images of these linear codes are new infinite families of minimal five-weight linear codes with wmin wmax < p-1 p . & COPY; 2023 Elsevier B.V. All rights reserved.
引用
收藏
页数：18
相关论文
共 50 条
  • [1] Linear codes from defining sets over Fp+ uFp and their applications
    Zeng, Xiangdi
    Zhang, Yaozong
    Gao, Jian
    COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (01)
  • [2] Several classes of linear codes with a few weights from defining sets over Fp plus uFp
    Liu, Haibo
    Liao, Qunying
    DESIGNS CODES AND CRYPTOGRAPHY, 2019, 87 (01) : 15 - 29
  • [3] Duadic codes over Fp plus uFp plus vFp plus uvFp
    Kumar, Raj
    Bhaintwal, Maheshanand
    FILOMAT, 2023, 37 (12) : 3985 - 3998
  • [4] On some special codes over Fp + uFp + u2Fp
    Cengellenmis, Y.
    APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (03) : 720 - 722
  • [5] Two and three weight codes over Fp + uFp
    Shi, Minjia
    Wu, Rongsheng
    Liu, Yan
    Sole, Patrick
    CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2017, 9 (05): : 637 - 646
  • [6] Few-weight linear codes over Fp from t-to-one mappings
    Rodriguez-Aldama, Rene
    FINITE FIELDS AND THEIR APPLICATIONS, 2024, 100
  • [7] Qadratic residue codes over Fp+uFp+vFP*
    Pathak, Sachin
    Ghosh, Gobinda
    Yadav, Bhanu P.
    Upadhyay, Ashish K.
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2021, 14 (10)
  • [8] Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications
    Liu, Haibo
    Liao, Qunying
    Wang, Xiaofeng
    JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2019, 32 (03) : 947 - 969
  • [9] Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications
    Haibo Liu
    Qunying Liao
    Xiaofeng Wang
    Journal of Systems Science and Complexity, 2019, 32 : 947 - 969
  • [10] Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications
    LIU Haibo
    LIAO Qunying
    WANG Xiaofeng
    Journal of Systems Science & Complexity, 2019, 32 (03) : 947 - 969
12345