# New weighing matrices and orthogonal designs constructed using two sequences with zero autocorrelation function – a review

@article{Koukouvinos1999NewWM, title={New weighing matrices and orthogonal designs constructed using two sequences with zero autocorrelation function – a review}, author={C. Koukouvinos and J. Seberry}, journal={Journal of Statistical Planning and Inference}, year={1999}, volume={81}, pages={153-182} }

Abstract The book, Orthogonal Designs : Quadratic Forms and Hadamard Matrices , Marcel Dekker, New York-Basel, 1979, by A.V. Geramita and Jennifer Seberry, has now been out of print for almost two decades. Many of the results on weighing matrices presented therein have been greatly improved. Here we review the theory, restate some results which are no longer available and expand on the existence of many new weighing matrices and orthogonal designs of order 2 n where n is odd. We give a number… Expand

#### 53 Citations

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Further results on ternary complementary sequences, orthogonal designs and weighing matrices

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- Australas. J Comb.
- 2011

A set of sequences is complementary, if the sum of their periodic or nonperiodic autocorrelation function is zero. Infinite families of orthogonal designs, based on some weighing matrices of order… Expand

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- Mathematics
- 2002

In this paper we use some results on weighing matrices W (2 n ,9) constructed using two circulants to obtain infinite classes of orthogonal designs. We also present a method that is used to construct… Expand

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In this paper we establish a fundamental link between the search for weighing matrices constructed from two circulants and the operation of sorting strings, an operation that has been studied… Expand

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- J. Comb. Optim.
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A modified power spectral density test is established that is applied to the search for weighing matrices of small weights constructed from two circulants to define the Discrete Fourier Transform on the support of the first rows of the twocirculants, thus exploiting the inherent sparsity of the problem. Expand

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In this paper, we demonstrate that the search for weighing matrices of small weights constructed from two circulants can be viewed as a string sorting problem together with a linear time algorithm to… Expand

NEW INFINITE CLASSES OF WEIGHING MATRICES

- Mathematics
- 2002

SUMMARY. In this paper we use a new algorithm to find weighing matrices W(2n;9) constructed using two circulant matrices. The basic idea of this algorithm is to investigate all possible ways the… Expand

When the necessary conditions are not sufficient: sequences with zero autocorrelation function

- Mathematics
- 1999

Recently K. T. Arasu (personal communication) and Yoseph Strassler, in his PhD thesis, The Classification of Circulant Weighing Matrices of Weight 9, Bar-Ilan University, Ramat-Gan, 1997, have… Expand

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- Computer Science
- Australas. J Comb.
- 2010

In this paper we present, infinite families of new orthgonal designs, based on some weighing matrices of order 2n, weight 2n k and spread o, constructed from two circlante and directed sequences.… Expand

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