Graphs and Combinatorics

, Volume 8, Issue 4, pp 317–321 | Cite as

CirculantGH(p2; Z p ) exist for all primesp

  • Warwick de Launey
Original Papers


The only known circulant ordinary Hadamard matrix is developed from the initial row-1, 1, 1, 1. Letp be a prime, and letZ p denote the cyclic group of orderp. In this paper, we construct circulantGH(p2;Z p ) for all primesp. Whenp is odd, this result also extends the earlier result that there exist circulantGH(p;Z p ) for all odd primesp. Other families ofGH-matrices which are developed modulo a group are discussed.


Early Result Cyclic Group Hadamard Matrix 


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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Warwick de Launey
    • 1
  1. 1.Cryptomathematics Group Communications Division, Electronic Research LaboratoryDefence Science and Technology OrganisationAustralia

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