One-weight and two-weight \(\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]\)-additive codes

  • Minjia ShiEmail author
  • Chenchen Wang
  • Rongsheng Wu
  • Yu Hu
  • Yaoqiang Chang
Part of the following topical collections:
  1. Special Issue on Sequences and Their Applications


In this paper, a class of additive codes which is referred to as \(\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]\)-additive codes is introduced. This is a generalization towards another direction of recently introduced \(\mathbb {Z}_{2}\mathbb {Z}_{4}\) codes (Doughterty et al., Appl. Algebra Eng. Commun. Comput. 27(2), 123–138, 2016). A MacWilliams-type identity that relates the weight enumerator of a code with its dual is proved. Furthermore, the structure and possible weights for all one-weight and two-weight \(\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]\)-additive codes are described. Additionally, we also construct some one-weight and two-weight \(\mathbb {Z}_{2}\mathbb {Z}_{2}[u,v]\)-additive codes to illustrate our obtained results.


Additive codes One-weight codes Two-weight codes MacWilliams identity 

Mathematics Subject Classification (2010)

94B05 94B15 



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Minjia Shi
    • 1
    Email author
  • Chenchen Wang
    • 1
  • Rongsheng Wu
    • 1
  • Yu Hu
    • 1
  • Yaoqiang Chang
    • 1
  1. 1.Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of MathematicsAnhui UniversityAnhuiPeople’s Republic of China

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