Norton Algebras of the Hamming Graphs via Linear Characters


 The Norton product is defined on each eigenspace of a distance regular graph by the orthogonal projection entry-wise product. resulting algebra, known as commutative nonassociative algebra that useful in group theory due to its interesting automorphism group. We provide formula for Hamming using linear characters. construct large subgroup automorphisms and completely describe some cases. also show possible, except special cases which it either associative or equally so-called double minus operation previously studied author, Mickey, Xu. Our results restrict hypercubes extend halved and/or folded cubes, bilinear forms graphs, more generally, all Cayley graphs finite abelian groups.