The Construction of Hadamard Matrices.
Final technical rept. 4 Jun-4 Sep 72,
TECHNOLOGY INC DAYTON OHIO
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A Hadamard matrix of size n is an n x n matrix H of plus or minus 1s for which H sup TH nI. Such a matrix can exist only when n1, n2, or n identically equal to 0 mod 4, in which case H sup TH has maximum possible determinant for any n x n matrix H with complex entries lying in the unit disc. It is a classic unsolved problem with many applications e.g. best weighing designs to provide constructions for all n identically equal to 0 mod 4 for which they exist. The author gives an essentially self-contained exposition of most of the known constructions of Hadamard matrices which are skew type or symmetric. The necessary auxiliary symmetric block designs, group difference sets, Szekeres difference sets, etc., are given in detail. Author
- Theoretical Mathematics