# Further explorations into ternary complementary pairs

@article{Craigen2006FurtherEI, title={Further explorations into ternary complementary pairs}, author={Robert Craigen and Stelios D. Georgiou and Will Gibson and Christos Koukouvinos}, journal={J. Comb. Theory, Ser. A}, year={2006}, volume={113}, pages={952-965} }

In [R. Craigen, C. Koukouvinos, A theory of ternary complementary pairs, J. Combin. Theory Ser. A 96 (2001) 358-375], we proposed a systematic approach to the theory of ternary complementary pairs (TCPs) and showed how all pairs known then could be constructed using a single elementary product, the natural equivalence relations, and a handful of pairs which we called primitive. We also introduced more new primitive pairs than could be inferred previously, concluding with some conjectures… Expand

#### 17 Citations

An update on primitive ternary complementary pairs

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2007

The state of the art with respect to primitive pairs is reported and some conjectures in light of new data are elaborate on, including a new refinement of the concept of primitivity. Expand

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

- Mathematics, Computer Science
- 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

Equivalence Between Certain Complementary Pairs of Types I and III

- Computer Science, Mathematics
- Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes
- 2009

This paper further characterises a class of type-I pairs defined over the alphabet {−1, 0, 1} and shows that a subset of these pairs are local-unitaryequivalent to a subsets of the type-III pairsdefined over a bipolar alphabet. Expand

LCD codes from weighing matrices

- Computer Science, Mathematics
- Applicable Algebra in Engineering, Communication and Computing
- 2019

This paper outlines a construction for LCD codes over finite fields of order q using weighing matrices and their orbit matrices, and proposes a decoding algorithm that can be feasible for the LCD codes obtained from some of the given methods. 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

On circulant and two-circulant weighing matrices

- Computer Science
- Australas. J Comb.
- 2010

New weighing matrices are constructed which are listed as open in the second edition of the Handbook of Combinatorial Designs and fill a missing entry in Strassler’s table with answer “YES”. Expand

Competent genetic algorithms for weighing matrices

- Mathematics, Computer Science
- J. Comb. Optim.
- 2012

In this paper, we demonstrate that the search for weighing matrices constructed from two circulants can be viewed as a minimization problem together with two competent genetic algorithms to locate… 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

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

A Novel Class of Periodic Complementary Sequence Sets over 8-QAM+ Constellation

- Physics
- 2014

Based on a ternary complementary sequence set \( {\text{PCS}}_{3}^{N,2M} \), the number and period of whose sub-sequences are 2M and N, respectively, and its reversal, we propose a method so as to… Expand

#### References

SHOWING 1-10 OF 16 REFERENCES

A Theory of Ternary Complementary Pairs

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2001

The basic theory of ternary complementary pairs is redeveloped, showing how to construct all known pairs from a handful of initial pairs the authors call primitive, and all primitive pairs up to length 14 are displayed, more than doubling the number that could be inferred from the existing literature. Expand

A complete description of Golay pairs for lengths up to 100

- Computer Science, Mathematics
- Math. Comput.
- 2004

In extending the theory of composition, this paper is able to obtain a closed formula for the number of pairs of length 2 k n generated by a primitive pair of length n, and identifies five primitive pairs. Expand

On ternary complementary pairs

- Mathematics, Computer Science
- Australas. J Comb.
- 2001

A variety of new constructions which concatenate shorter groups of sequences to obtain longer sequences to give many new restrictions on TCP's of lengths £ and deficiencies 8 = 2x, where x == £ mod 4. Expand

On Golay sequences

- Computer Science, Mathematics
- Discret. Math.
- 1991

It is proved that Golay sequences of length n = 2 · 7 2 t do not exist and new proofs of some known results are given and conjecture that there are no Golays of length 2 · q 2 t where q is not the sum of two integer squares. Expand

On ternary complementary sequences

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1994

A new family of complementary pairs of sequences over the alphabet /spl alpha//sub 3/=+{1,-1,0}. Expand

On Golay polynomial pairs

- Mathematics
- 1991

In this article, we study Golay polynomial pairs, a notion arising in various fields such as optics, engineering, combinatorics, and Fourier analysis.

Static multislit spectrometry and its application to the panoramic display of infrared spectra.

- Physics, Medicine
- Journal of the Optical Society of America
- 1951

The rate at which information about infrared spectra can be obtained in this manner is illustrated by a photograph of the CO2 spectrum which includes both the 14μ and 15μ absorption bands, and which was obtained in 100 milliseconds. Expand

Products and factorizations of ternary complementary pairs

- Mathematics, Computer Science
- Australas. J Comb.
- 2006

Using affixes to search for TCPs

- preparation
- 2005

Using affixes to search for TCPs, in preparation

- Using affixes to search for TCPs, in preparation
- 2005