The minimum distance of new generalisations of the punctured binary Reed-Muller codes

  • Liqin HuEmail author
  • Keqin Feng


In 2018, Ding et al. introduced a new generalisation of the punctured binary Reed-Muller codes to construct LCD codes and 2-designs. They studied the minimum distance of the codes and proposed an open problem about the minimum distance. In this paper, several new results on the minimum distance of the generalised punctured binary Reed- Muller are presented. Particularly, some of the results are a generalisation or improvement of previous results in (Finite Fields Appl. 53, 144–174, 2018).


Reed-Muller code Generalized Reed-Muller code Cyclic code 

Mathematics Subject Classification (2010)

94B05 94B15 94B65 



The authors are very grateful to the reviewers for their comments that improved the quality of this paper.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.School of CyberspaceHangzhou Dianzi UniversityHangzhouChina
  2. 2.Department of Mathematical ScienceTsinghua UniversityBeijingChina

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