Constructions for hadamard matrices using Clifford algebras, and their relation to amicability/anti-amicability graphs

It is known that the Williamson construction for Hadamard matrices can be generalized to constructions using sums of tensor products. This pa-per describes a specific construction using real monomial representations of Of Clifford algebras, and its connection with graphs of amicability and anti-amicability. It is proven that this construction works for all such representations where the order of the matrices is a power of 2. Some related results are given for small dimensions.