There are several non-associative finite dimensional division algebras over different number fields. Their representations in the corresponding matrix algebras preserve additive structure. However, the embedding does not preserve multiplication as matrix multiplication is associative. As such, it gives a generalized matrix representation. Indeed, a non-associative structure provides different platforms for more effective and useful space-time coding satisfying rank criteria, and coding gain criteria for multiple antenna wireless communication. Associative division algebras have dimension restrictions, whereas non-associative division algebras over suitable fields exist in infinitely many dimensions. We illustrate the above program by using octonion algebras.