Association schemes related to Delsarte-Goethals codes

Abstract

In this paper, we construct an infinite series of 9-class association schemes from a refinement of the partition of Delsarte-Goethals codes by their Lee weights. The explicit expressions of the dual schemes are determined through direct manipulations of complicated exponential sums. As a byproduct, another three infinite families of association schemes are also obtained as fusion schemes and quotient schemes. © 2014 Springer Science+Business Media New York.