Equivalence classes of n-dimensional proper Hadamard matrices

Equivalence operations for n-dimensional proper Hadamard matrices are defined. Their equivalence classes are investigated and bounds on the number of such equivalence classes are found to be associated with the number of equivalence classes of 2-dimensional Hadamard matrices. Properties of planes (2-dimensional sections) in an n-dimensional proper Hadamard matrix are investigated. It is shown that all planes of an ndimensional proper Hadamard matrix are Hadamard equivalent to the 2-dimensional Hadamard matrix from which it is constructed, regardless of whether the construction technique applied is Product Construction, Group Development or Relative Difference Set Construction. The relationship of the three constructions is demonstrated.