Construction of binary linear codes via rational function fields

被引：1
作者：
Jin, Lingfei [1 ]
Kan, Haibin [1 ]
机构：
[1] Fudan Univ, Shanghai Key Lab Intelligent Informat Proc, Sch Comp Sci, Shanghai 200433, Peoples R China
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2017年 / 83卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Rational function fields; Binary linear codes; Places;
D O I：
10.1007/s10623-016-0252-1
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
By employing a certain multiplicative group in the rational function field and places of degree one and two, we present a construction of binary linear codes in this paper. One feature is that the minimum distance of the code is bounded via the Hurwitz genus formula of function fields. It turns out that many optimal and best-known binary linear codes are obtained through our construction.
引用
收藏
页码：633 / 638
页数：6
相关论文
共 44 条
  • [31] 3 BEST BINARY LINEAR BLOCK-CODES OF MINIMUM DISTANCE 15
    FARKAS, P
    BRUHL, K
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1994, 40 (03) : 949 - 951
  • [32] ADMM-Based Decoder for Binary Linear Codes Aided by Deep Learning
    Wei, Yi
    Zhao, Ming-Min
    Zhao, Min-Jian
    Lei, Ming
    IEEE COMMUNICATIONS LETTERS, 2020, 24 (05) : 1028 - 1032
  • [33] ON MAXIMUM-LIKELIHOOD SOFT-DECISION DECODING OF BINARY LINEAR CODES
    LOUS, NJC
    BOURS, PAH
    VANTILBORG, HCA
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1993, 39 (01) : 197 - 203
  • [34] Binary Linear Codes With Few Weights From Two-to-One Functions
    Li, Kangquan
    Li, Chunlei
    Helleseth, Tor
    Qu, Longjiang
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2021, 67 (07) : 4263 - 4275
  • [35] ALL BINARY LINEAR CODES OF LENGTHS UP TO 18 OR REDUNDANCY UP TO 10 ARE NORMAL
    Baicheva, Tsonka
    ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2011, 5 (04) : 681 - 686
  • [36] Infinite towers of Artin-Schreier defect extensions of rational function fields
    Blaszczok, Anna
    VALUATION THEORY IN INTERACTION, 2014, : 16 - 54
  • [37] The sixth power moment of Dirichlet L-functions over rational function fields
    Djankovic, Goran
    Dokic, Dragan
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 514 (01)
  • [38] Multisequences With Large Linear and k-Error Linear Complexity From Hermitian Function Fields
    Xing, Chaoping
    Ding, Yang
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (08) : 3858 - 3863
  • [39] A Simulation Study on Decoding of Binary Linear Codes Using Projective Geometry PG(3,2)
    Gokpinar, Fikri
    GAZI UNIVERSITY JOURNAL OF SCIENCE, 2007, 20 (04): : 127 - 132
  • [40] At most three-weight binary linear codes from generalized Moisio’s exponential sums
    Yansheng Wu
    Qin Yue
    Xueying Shi
    Designs, Codes and Cryptography, 2019, 87 : 1927 - 1943
12345