THE HIDDEN CIRCULANT MATRICES



© Nickolay Balonin and Jennifer Seberry, 1.05.2014

Conference matrix catalogue and on-line algorithms


1. N. A. Balonin, Jennifer Seberry A Review and New Symmetric Conference Matrices //Informatsionno-upravliaiushchie sistemy, 2014, № 4 (71), pp. 2–7.

ILLUSTRATIONS TO MATHON'S-TYPE MATRICES


Balonin-Seberry construction of Mathon's type CORE C46=circul(A,B,C,C',B') has rich cell-structure: A is a circulant matrix of circulant cells (1-type), B is a circulant matrix of back-circulant cells (2-type), C is a cross-matrix (0-type)), the core of order n=q2(q+2), where q+2 is order of a core, q=3.



Matrices A, B, C of rich-structure C46


Block A=circul(a,b,c) has cells a=circul([0 1 1]), b=circul([-1 -1 1]), c=b'=circul([-1 1 -1]) based on the Legendre symbols of core C10 (Paley case).

Observe A=circul(a,b,c) with cells a=a|0→1, b=–a, c=–c based on the sign-conjugated Legendre symbols and B, C as blocks with hidden circulant cells: B=L1AR1, C=–L2BR2 built by permutation matrices:



Permutation matrices L1, R1, L2, R2 of the hidden circulant structure



THE MULTICIRCULANT FORM OF C46



ILLUSTRATIONS TO THE PAPER | ON LINE ALGORITHMS

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