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Periodic Golay Pairs of Length 72

  • Dragomir Ž.-Doković
  • Ilias S. Kotsireas
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 133)

Abstract

We construct supplementary difference sets (SDSs) with parameters (72; 36, 30; 30). These SDSs give periodic Golay pairs of length 72. No periodic Golay pair of length 72 was known previously. The smallest undecided order for periodic Golay pairs is now 90. The periodic Golay pairs constructed here are the first examples having length divisible by a prime congruent to 3 modulo 4. The main tool employed is a recently introduced compression method. We observe that Turyn’s multiplication of Golay pairs can be also used to multiply a Golay pair and a periodic Golay pair.

Keywords

Ordinary and periodic Golay pairs Supplementary difference sets Compression method 

Notes

Acknowledgements

The authors wish to acknowledge generous support by NSERC. This research was enabled in part by support provided by WestGrid (www.westgrid.ca) and Compute Canada Calcul Canada (www.computecanada.ca). We thank a referee for his suggestions.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooONCanada
  2. 2.Department of Physics & Computer ScienceWilfrid Laurier UniversityONCanada

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