30×30 {-1, +1} matrices of maximal determinant

|Det R_j| = 19668469112621×2²⁹ = 203×7¹³×2²⁹ for j=1, 2 , 3

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

M=R_j^TR_j= R_j R_j^T for j=1, 2 , 3:

    | S   0 |
M = |       |
    | 0   S |

with S = 28 I + 2 J where I is the 15×15 identity matrix and J is the 15×15 matrix with all entries 1.

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:

A maximal determinant was first reported by Ehlich [E1].
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.
Are there other inequivalent matrices not in the form of circulant blocks?

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This page created 10 March 2002.