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MacDonald codes over the ring \({\mathbb {F}}_{p}+v{\mathbb {F}}_{p}+v^2{\mathbb {F}}_{p}\)

  • Yongkang Wang
  • Jian GaoEmail author
Article

Abstract

In this paper, we consider MacDonald codes over the finite non-chain ring \({\mathbb {F}}_p+v{\mathbb {F}}_p+v^2{\mathbb {F}}_p\) and their applications in constructing secret sharing schemes and association schemes, where p is an odd prime and \(v^3=v\). We give some structural properties of MacDonald codes first. Then, we study the weight enumerators of torsion codes of these MacDonald codes. As some applications, constructing secret sharing schemes and association schemes is also investigated.

Keywords

MacDonald codes Torsion codes Secret sharing schemes Association schemes 

Mathematics Subject Classification

94B05 11T71 

Notes

Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant Nos. 11701336, 11626144 and 11671235), and the Scientific Research Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (No. 2018MMAEZD04).

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsShandong University of TechnologyZiboPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsChangsha University of Science and TechnologyChangshaPeople’s Republic of China

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