Designs, Codes and Cryptography

, Volume 87, Issue 2–3, pp 327–340 | Cite as

Combinatorial metrics: MacWilliams-type identities, isometries and extension property

  • Jerry Anderson Pinheiro
  • Roberto Assis Machado
  • Marcelo FirerEmail author
Part of the following topical collections:
  1. Special Issue: Coding and Cryptography


In this work we characterize the combinatorial metrics admitting a MacWilliams-type identity and describe the group of linear isometries of such metrics. Considering the binary case, we classify the metrics satisfying the MacWilliams extension property (for disconnected coverings) and give a necessary condition for the extension property (for connected coverings).


Combinatorial metric MacWilliams identity Extension of isometries 

Mathematics Subject Classification

94A24 51E22 



The authors would like to thank the São Paulo Research Foundation (Fapesp) for the financial support through three Grants: 2013/25977-7, 2017/14616-4 and 2017/10018-5.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics, Statistics and Scientific ComputingUniversity of CampinasCampinasBrazil

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