26×26 {-1, +1} matrices of maximal determinant

|Det Rj| = 54419558400×225 = 150×611×225 for j=1, 2 , 3

Ratio of |Det Rj| to Ehlich/Wojtas bound: 1

M=RjTRj= Rj RjT for j=1, 2 , 3: 

26  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2 26  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2 26  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2 26  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2 26  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2 26  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 26  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2 26  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2 26  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2  2 26  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2  2  2 26  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2  2  2  2 26  2  0  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2  2  2  2  2 26  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  0 26  2  2  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2 26  2  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2 26  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2 26  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2 26  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2 26  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2 26  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2 26  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2 26  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2 26  2  2  2 
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2 26  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2 26  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2 26

There are three inequivalent matrices composed of circulant blocks, A and B:

 | A   B |
 |       |
 |  T   T|
 |-B   A |
The first rows of A and B are:
R1: 
+++++++-++--+      ++---+-++-+-+
R2: 
+++++++-++--+      +++--+-+-+--+
R3: 
++++-+--+++-+      ++++-+--+++-+

Notes:

  1. A maximal determinant was first reported by Ehlich [E1] and by Wojtas [Wo].
  2. The complete set of circulant block forms was found by Yang [Y3]. That there are three inequivalent ones was shown by Kounias, Koukouvinos, Nikolaou and Kakos [KKNK1] who gave the forms listed here.
  3. Are there other inequivalent matrices not in the form of circulant blocks?
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This page created 10 March 2002.