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(p 2;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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brock, B.: A new construction of circulantGH(p 2;Z p )s.Discrete Math. (to appear) (1992)
Butson, A.T.: Relations among generalised Hadamard matrices, relative difference sets and maximal length linear recurring sequences,Can. J. Math. 15, 42–48 (1963)
de Launey, W.: A survey of generalised Hadamard matrices and difference matrices with larger, Utilitas Mathematica,30, 5–29 (1986)
de Launey, W.: Generalised Hadamard matrices which are developed modulo a group,Discrete Math., (to appear) (1992)
Elliott, J.E.H. and Butson, A.T.: Relative difference sets,Illinois J. Math. 10, 517–531 (1966)
Jungnickel, D.: On automorphism groups of divisible designs,Can. J. Math. 34, 257–297 (1982)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
de Launey, W. CirculantGH(p 2; Z p ) exist for all primesp . Graphs and Combinatorics 8, 317–321 (1992). https://doi.org/10.1007/BF02351588
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02351588