REGULAR SUBOPTIMAL MATRICES



Hadamard matrix family catalogue and on-line algorithms

© Nickolay A. Balonin, 1.05.2014


Regular suboptimal Matrix Congecture. A regular quasi-orthogonal matrix of order n with (n+1)/2 moduli of levels with n-elements: x1=1, |x2|, ..., |x(n+1)/2| (numbers can be equal to eath-other) has weight near to maximum. Some of them are maximum determinant (i.e. optimal) regular quasi-orthogonal matrices.



Optimal regular Cretan(1;1;1) and histogram of its moduli



Optimal regular Cretan(3;2;2.25) and histogram of its moduli



Optimal regular Cretan(5;3;3.3611) and histogram of its moduli



Optimal regular Cretan(7;4;5.0294) and histogram of its moduli



Optimal BM-matrix(7;5;5.0777) and Optimal regular Cretan(7;4;5.0294)



Optimal regular Cretan(9;5;6.4024) and histogram of its moduli



Optimal BM-matrix(9;4;6.4308) and Optimal regular Cretan(9;5;6.4024)



Optimal regular Cretan(11;6;8.5022) and histogram of its moduli



Optimal regular Cretan(13;7;8.3734) and histogram of its moduli

Optimal Balonin-Mironovski – Cretan(7;5;30,6,3,4,6;5.0777)
first row and column d,b,b,b,a,a,a;
core [[backcirc(–a,e,–c), circ(–a,a,a)],[circ(–a,a,a), backcirc(e,–a,–d)]];
Suboptimal regular Cretan(7;4;5.0294)
circ(x1,x1,x1,–x2,x1,–x3,–x4) where x1=1; x2=x3=x4=b
Optimal Balonin-Mironovski – Cretan(9;4;40,16,24,1;6.4308)
first row and column –d,b,b,b,b,b,b,b,b; core circ(a,–a,c,c,a,c,–a,–a);
Suboptimal regular Cretan(9;5;6.4024) is block back circulant with cells
back circ(a,a,e); back circ(–a,–d,c); back circ(a,a,–b)
The initial block is shifted back circ(e,a,a).


STRONG OPTIMAL MATRICES



Optimal BM-matrix(7;5;5.0777) and BM-matrix(9;4;6.4308)

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