Advertisement

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

Abstract

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.

Keywords

Early Result Cyclic Group Hadamard Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations