An octonion algebra originating in combinatorics

Abstract

C.H. Yang discovered a polynomial version of the classical Lagrange identity expressing the product of two sums of four squares as another sum of four squares. He used it to give short proofs of some important theorems on composition of δ \delta -codes (now known as T T -sequences). We investigate the possible new versions of his polynomial Lagrange identity. Our main result shows that all such identities are equivalent to each other.