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Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications

  • Haibo Liu
  • Qunying LiaoEmail author
  • Xiaofeng Wang
Article
  • 6 Downloads

Abstract

Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an odd prime p, the complete weight enumerator of a class of p-ary linear codes based on defining sets are determined. Furthermore, from the explicit complete weight enumerator of linear codes, a new class of optimal constant composition codes and several classes of asymptotically optimal systematic authentication codes are obtained.

Keywords

Authentication codes complete weight enumerator constant composition codes exponential sums linear codes secret sharing schemes weight distributions 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics and Software ScienceSichuan Normal UniversityChengduChina
  2. 2.College of Mathematics and StatisticsShenzhen UniversityShenzhenChina

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