NEGACYCLIC WEIGHING MATRICES

© Nickolay A. Balonin, Dragomir Z. Djokovic, 22.04.2015

Hadamard-type matrix catalogue and on-line algorithms

 PALEY MATRICES WILLAMSON MATRICES

2-NEGACYCLIC WEIGHING MATRICES

2N-W(n,n–2) and 2N-W(n,n–4)

GOLAY-PALEY/GOLAY CODES MULTIPLIER

NUMERICAL ALGORITHM 2N W(n,nk)

GALOIS FIELD ALGORITHM 2N W(n,nk)

2C MATRICES: n=4+k*16, n=12+k*16

2-TOEPLITZ WEIGHING MATRICES LIBRARY

2N-W(n,n–3) and 2N-W(n,n–4)

1-NEGACYCLIC WEIGHING MATRICES

Specifical N1-construction W(n,n–2)=[A B;–B A], based on two non orthogonal (!) Toeplitz blocks A, B, where 1-column of B is reversed and shifted 1-row of A, 1-row of B is reversed and shifted the inversed 1-column of A.

N1-MATRICES WITH SYMMETRIES

Correlation with Blue P, Red GP, Yellow 2GP-A, D

WEIGHING MATRICES n=4+16*k

Weighing matrices W(n,n–2), n=4+16*k, 4, 20, 36!, 52, [68?], 84, 100?, .. with two zeros, giving two negacyclic Hadamard H2n=[A B;B' –A'] or zipper H*2n=[A B;B –A] matrices. Lenght v=n/2=34 can be crytical for these matrices, so order 68 is under doubts.

TWO NEGACYCLIC VERSIONS H2n=[A B;B' –A']

Weighing matrices W(4,2) and H8

Weighing matrices W(20,18) and H40

Weighing matrices W(36,34) and H72

Weighing matrices W(52,50) and H104

Weighing matrices W(52,50)

Weighing matrices W(84,82) and H168

Weighing matrices W(100,98) and H200

ZIPPER VERSION H*72=[A B;B –A]

Weighing matrices W(36,34) and H*72

WEIGHING MATRICES n=12+16*k

Weighing matrices W(n,n–2), n=12+16*k, 12, 28, [44?], 60, 76, [92?], 108?, .. with two zeros, giving two negacyclic Hadamard H2n=[A B;B' –A'] or zipper H*2n=[A B;B –A] matrices. Lenghts v=n/2=22 and 46 can be crytical for these matrices, so orders 44 and 92 are under doubts.

Weighing matrices W(12,10) and H24

Weighing matrices W(28,26) and H56

Weighing matrices W(60,58) and H120

Weighing matrices W(76,74) and H152

ZIPPER VERSIONS

Weighing matrices W(12,10) and H*12

Weighing matrices W(28,26) and H*28

GALOIS FIELD CALCULATIONS

Calculate N1 as [A B;–B A], A,B – Toeplitz blocks; we tie A-block with NPG-pair, then find B (GF(p2), p=4*t–1).

Calculate N1 as [A B;–B A], A,B – Toeplitz blocks; we tie A-block with NPG-pair, then find B (GF(p2), p=2*t–1).

Similar by sense W(n,n–2) matrix, based on two nega-circulant blocks.

Prove a root

By two C-matrices:

By shift

VITOLD (NEGA-CYCLIC C-MATRICES) | JANKO (BLOCKS OF BUSH-TYPE HM)

НОВЫЙ АЛГОРИТМ ПОИСКА

С произвольной выборкой

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