Accession Number : AD0765208

Title :   The Construction of Hadamard Matrices.

Descriptive Note : Final technical rept. 4 Jun-4 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 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)

Descriptors :   (*MATRICES(MATHEMATICS), PERMUTATIONS), NUMBER THEORY, GROUPS(MATHEMATICS), SET THEORY, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE