# A Theory of Ternary Complementary Pairs

@article{Craigen2001ATO, title={A Theory of Ternary Complementary Pairs}, author={R. Craigen and C. Koukouvinos}, journal={J. Comb. Theory, Ser. A}, year={2001}, volume={96}, pages={358-375} }

Sequences with zero autocorrelation are of interest because of their use in constructing orthogonal matrices and because of applications in signal processing, range finding devices, and spectroscopy. Golay sequences, which are pairs of binary sequences (i.e., all entries are ±1) with zero autocorrelation, have been studied extensively, yet are known only in lengths 2a10b26c. Ternary complementary pairs are pairs of (0, ±1)-sequences with zero autocorrelation (thus, Golay pairs are ternary… Expand

#### 25 Citations

Boolean and ternary complementary pairs

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2003

An exhaustive survey of pairs of small lengths and construct some infinite classes clearly of fundamental importance in the theory, which completely characterize all pairs of even weight and give a product construction for pairs of odd weight that gives a greater variety of new pairs than similar product methods used in the ternary case. Expand

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

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- Australas. J Comb.
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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

Generation and correlation algorithms for ternary complementary pairs of sequences of length 3·2n

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- Int. J. Circuit Theory Appl.
- 2015

Algorithms for generating and performing the correlation of ternary complementary pairs using a minimum amount of calculations are described, making it possible to attain a wider range of lengths, and, as a consequence, a widerrange of noise immunity in some applications. Expand

Good code sets

- Computer Science, Mathematics
- 2011 3rd International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT)
- 2011

A new class of sparse mutually orthogonal optical codes is introduced, based on defining the separation between nonzero elements via logarithms of powers of prime numbers, particularly suited for soliton based optical codes. Expand

Good code sets by spreading orthogonal vectors via Golomb rulers and Costas arrays

- Mathematics
- 2010 IEEE Radar Conference
- 2010

Good code sets have autocorrelation functions ACF with small sidelobes, and also have small crosscorrelations. In this work, a class of good ternary codes sets are introduced. First, mutually… Expand

Further explorations into ternary complementary pairs

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2006

This paper investigates patterns among those lengths and weights that are within easy computational distance from the last length considered therein, length 14, and provides support for the previous conjectures, and shed enough new light to speculate further as to the likely ultimate shape of the theory. Expand

Contemporary Mathematics What can be used instead of a Barker sequence ?

- 2007

A classical problem of digital sequence design, first studied in the 1950s but still not well understood, is to determine long binary sequences for which the absolute values of the aperiodic… Expand

Generalised Complementary Arrays

- Computer Science, Mathematics
- IMACC
- 2011

This work presents a generalised setting for the construction of complementary array pairs and its proof, using unitary matrix notation, and derives closed-form Boolean formulas for these cases. Expand

A multi-dimensional approach to the construction and enumeration of Golay complementary sequences

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2008

This process greatly simplifies previous approaches, by separating the construction of Golay arrays from the enumeration of all possible projections of these arrays to lower dimensions. Expand

ON THE COMPUTATION OF THE NON-PERIODIC AUTOCORRELATION FUNCTION OF TWO TERNARY SEQUENCES AND ITS RELATED COMPLEXITY ANALYSIS

- Mathematics
- 2011

We establish a new formalism of the non-periodic autocorrelation function (NPAF) of two sequences, which is suitable for the computation of the NPAF of any two sequences. It is shown, that this… Expand

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