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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  1. 1.
    Brock, B.: A new construction of circulantGH(p 2;Z p)s.Discrete Math. (to appear) (1992)Google Scholar
  2. 2.
    Butson, A.T.: Relations among generalised Hadamard matrices, relative difference sets and maximal length linear recurring sequences,Can. J. Math. 15, 42–48 (1963)MATHMathSciNetGoogle Scholar
  3. 3.
    de Launey, W.: A survey of generalised Hadamard matrices and difference matrices with larger, Utilitas Mathematica,30, 5–29 (1986)MATHMathSciNetGoogle Scholar
  4. 4.
    de Launey, W.: Generalised Hadamard matrices which are developed modulo a group,Discrete Math., (to appear) (1992)Google Scholar
  5. 5.
    Elliott, J.E.H. and Butson, A.T.: Relative difference sets,Illinois J. Math. 10, 517–531 (1966)MathSciNetGoogle Scholar
  6. 6.
    Jungnickel, D.: On automorphism groups of divisible designs,Can. J. Math. 34, 257–297 (1982)MATHMathSciNetGoogle Scholar

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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