
Accession Number : AD0765208
Title : The Construction of Hadamard Matrices.
Descriptive Note : Final technical rept. 4 Jun4 Sep 72,
Corporate Author : TECHNOLOGY INC DAYTON OHIO
Personal Author(s) : Payne,Stanley E.
Report Date : JUL 1973
Pagination or Media Count : 96
Abstract : A Hadamard matrix of size n is an n x n matrix H of plus or minus 1's for which (H sup T)H = nI. Such a matrix can exist only when n=1, n=2, or n identically equal to 0 (mod 4), in which case (H sup T)H 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 selfcontained 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)
Descriptors : (*MATRICES(MATHEMATICS), PERMUTATIONS), NUMBER THEORY, GROUPS(MATHEMATICS), SET THEORY, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE