Paley partial difference sets in groups of order n4 and 9n4 for any odd n1

Authors:
John Polhill
Affiliations:
Department of Mathematics, Computer Science, and Statistics, Bloomsburg University, Bloomsburg, PA 17815, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2010

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Abstract

A partial difference set with parameters (v,v-12,v-54,v-14) is said to be of Paley type. In this paper, we give a recursive theorem that for all odd n1 constructs Paley partial difference sets in certain groups of order n^4 and 9n^4. We are also able to construct Paley-Hadamard difference sets of the Stanton-Sprott family in groups of order n^4(n^4+/-2) when n^4+/-2 is a prime power and 9n^4(9n^4+/-2) when 9n^4+/-2 is a prime power. Many of these are new parameters for such difference sets, and also give new Hadamard designs and matrices.