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.
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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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Dedicated to Hadi Kharaghani on the occasion of his 70th birthday
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Ž.-Doković, D., Kotsireas, I.S. (2015). Periodic Golay Pairs of Length 72. In: Colbourn, C. (eds) Algebraic Design Theory and Hadamard Matrices. Springer Proceedings in Mathematics & Statistics, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-319-17729-8_7
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DOI: https://doi.org/10.1007/978-3-319-17729-8_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17728-1
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