Association Schemes for Some Finite Group Rings II

Abstract

Association schemes have been used in coding theory and other combinatorial problems. In this paper, we construct association schemes for the abelian groups Z_2^r,〖 Z〗_(n_1 )×Z_(n_2 )×⋯×Z_(n_r ), set of n ×n matrices over Z_m and for the general linear group of order 2 over Z_2,Z_4, and Z_6. We also obtain association schemes for symmetric groups and alternating groups of degree 4 and 5 using canonical forms.