2005/11/06 by William P. Orrick, Orrick, William P.
Decision Sciences · Engineering · Mathematics · #05B20 #05B30 #62K05 #Combinatorics (math.CO) #FOS: Mathematics #Manufacturing Process and Optimization #Optimal Experimental Design Methods #Statistics Theory (math.ST) #graph theory and CDMA systems #math.CO #math.ST #msc:05B20 #msc:05B30 #msc:62K05 #stat.TH
paper · pdf · doi:10.48550/arxiv.math/0511141
11 pages; Introduction rewritten; final section split into two and expanded slightly
openalex publication_date 2005/11/06 · arxiv created 2006/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two matrices with elements taken from the set -1,1 are Hadamard equivalent if one can be converted into the other by a sequence of permutations of rows and columns, and negations of rows and columns. In this paper we summarize what is known about the number of equivalence classes of matrices having maximal determinant. We establish that there are 7 equivalence classes for matrices of order 21 and that there are at least 9,884 equivalence classes for matrices of order 26. The latter result is obtained primarily using a switching technique for producing new designs from old.