The Plotkin-Type Bound on the Generalized Symbol-Pair Weight and Symbol-Pair Equiweight Codes

被引：0
|
作者：
Liang, Yinghao [1 ]
Liu, Zihui [1 ,2 ]
机构：
[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China
[2] Beijing Inst Technol, Key Lab Math Theory & Computat Informat Secur, Beijing 100081, Peoples R China
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2024年 / 70卷 / 07期
基金：
北京市自然科学基金;
关键词：
Codes; Vectors; Measurement; Graph theory; Generators; Linear programming; Linear codes; Symbol-pair weight; generalized value assignment; Plotkin-type bound; block intersection graph; Hamilton cycle; HAMMING WEIGHTS;
D O I：
10.1109/TIT.2024.3392744
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We present the Plotkin-type bound on the generalized symbol-pair weight and show that all the symbol-pair equiweight codes achieve the Plotkin-type bound. Some new judging criteria are given for symbol-pair equiweight codes, and based on these judging criteria, we show the existence of a class of symbol-pair equiweight codes by design and graph theory. Also, we explicitly construct the symbol-pair version simplex code by the action of a group on a set. Furthermore, we construct several classes of inequiweight codes achieving the Plotkin-type bound.
引用
收藏
页码：4990 / 5001
页数：12
相关论文
共 50 条
  • [21] Function-Correcting Codes for Symbol-Pair Read Channels
    Xia, Qingfeng
    Liu, Hongwei
    Chen, Bocong
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (11) : 7807 - 7819
  • [22] On symbol-pair distances of repeated-root constacyclic codes of length 2ps over Fpm + uFpm and MDS symbol-pair codes
    Dinh, Hai Q.
    Singh, Abhay Kumar
    Thakur, Madhu Kant
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2023, 34 (06) : 1027 - 1043
  • [23] On symbol-pair weight distribution of MDS codes and simplex codes over finite fields
    Ma, Junru
    Luo, Jinquan
    CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2021, 13 (01): : 101 - 115
  • [24] Bounds and Constructions of Codes Over Symbol-Pair Read Channels
    Elishco, Ohad
    Gabrys, Ryan
    Yaakobi, Eitan
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (03) : 1385 - 1395
  • [25] Sliding window symbol-pair constrained codes for energy harvesting
    Kumar, Narendra
    Bhoi, Siddhartha Siddhiprada
    Gupta, Ruchir
    Singh, Abhay Kumar
    ANNALS OF TELECOMMUNICATIONS, 2023, 78 (1-2) : 71 - 77
  • [26] Constacyclic Symbol-Pair Codes: Lower Bounds and Optimal Constructions
    Chen, Bocong
    Lin, Liren
    Liu, Hongwei
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2017, 63 (12) : 7661 - 7666
  • [27] Maximum Distance Separable Codes for Symbol-Pair Read Channels
    Chee, Yeow Meng
    Ji, Lijun
    Kiah, Han Mao
    Wang, Chengmin
    Yin, Jianxing
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (11) : 7259 - 7267
  • [28] Decoding of Cyclic Codes over Symbol-Pair Read Channels
    Yaakobi, Eitan
    Bruck, Jehoshua
    Siegel, Paul H.
    2012 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT), 2012,
  • [29] Bounds and Constructions of Codes over Symbol-Pair Read Channels
    Elishco, Ohad
    Gabrys, Ryan
    Yaakobi, Eitan
    2018 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2018, : 2505 - 2509
  • [30] Sliding window symbol-pair constrained codes for energy harvesting
    Narendra Kumar
    Siddhartha Siddhiprada Bhoi
    Ruchir Gupta
    Abhay Kumar Singh
    Annals of Telecommunications, 2023, 78 : 71 - 77
12345