New weighing matrices via partitioned group actions

Radel Ben-Av, Giora Dula, Assaf Goldberger, Ilias Kotsireas, Yossi Strassler

Research output: Contribution to journalArticlepeer-review


We solve the smallest four open cases of weighing matrices, W(n,16) for n=23,25,27,29, which completes the existence question for weight 16. In addition we solve the open two-core matrix W(102,97). There is a common theme for the construction of all such matrices, which is called here partitioned group matrices. The study of partitioned group matrices generalizes some well known constructions, namely the one-core and two-core circulant constructions, with or without borders, block circulant matrices, Legendre pairs and many more. Such constructions generalize to arbitrary groups and carry an algebraic structure which we analyze in some cases. Our methods here can be made practical for larger weighing matrices. We also add a complete analysis of the possible location of the zeros (crystal sets) in two-core weighing matrices of co-weight 5.

Original languageEnglish
Article number113908
JournalDiscrete Mathematics
Issue number5
StatePublished - May 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.


  • Autocorrelation
  • Crystal sets
  • Cyclotomy
  • Partitioned matrices
  • Weighing matrices


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