Association schemes related to Delsarte-Goethals codes

TL;DR

This paper constructs new infinite families of association schemes from Delsarte-Goethals codes by refining partitions based on Lee weights, and explicitly determines their dual schemes.

Contribution

It introduces a novel method to derive multiple association schemes from Delsarte-Goethals codes using weight-based partition refinements.

Findings

Constructed 9-class association schemes from Delsarte-Goethals codes.

Explicit expressions for dual schemes were obtained.

Additional association schemes were derived as fusion and quotient schemes.

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, the other three infinite families of association schemes are also obtained as fusion schemes and quotient schemes.