Perfect Sequences and Arrays over the Unit Quaternions

The quaternions were discovered by the Irish mathematician Sir William Rowan Hamilton in 1843. Hamilton was interested in the connection between complex numbers and 2-dimensional geometry. He tried in vain to extend the complex numbers to R, only years later would it be discovered that there is no 3-dimensional normed division algebra. Hamilton’s breakthrough came when he extended the complex numbers to 4 dimensions. The quaternions are a 4-dimensional non-commutative division algebra. They can be thought of as an extension of the complex numbers, where