Weight Distribution of a Class of Linear Codes

• ZHANG Xina

  College of Mathematics and Statistics, Northwest Normal University Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology

• DU Xiaoni

  College of Mathematics and Statistics, Northwest Normal University

• WANG Rong

  College of Mathematics and Statistics, Northwest Normal University

• ZHANG Fujun

  College of Mathematics and Statistics, Northwest Normal University

抄録

Linear codes with a few weights have many applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs, and they are also of importance in consumer electronics, communications and data storage systems. In this paper, based on the theory of defining sets, we present a class of five-weight linear codes over $\mathbb{F}_p$(p is an odd prime), which include an almost optimal code with respect to the Griesmer bound. Then, we use exponential sums to determine the weight distribution.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E104.A (2), 399-403, 2021-02-01

  一般社団法人 電子情報通信学会

キーワード

• linear codes
• Gauss sums
• weight distribution

詳細情報

• CRID: 1391412881287333888
• NII論文ID: 130007978983
• DOI: 10.1587/transfun.2020sdp0003
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E104.A/2/E104.A_2020SDP0003/_pdf
• 本文言語コード: en
• データソース種別:
  • JaLC
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可