Abstract
This paper examines a pair of bent functions on \(\mathbb{Z}_{2}^{2m}\) and their relationship to a necessary condition for the existence of an automorphism of an edge-coloured graph whose colours are defined by the properties of a canonical basis for the real representation of the Clifford algebra \(\mathbb{R}_{m,m}.\) Some other necessary conditions are also briefly examined.
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Acknowledgements
This work was first presented at the Workshop on Algebraic Design Theory and Hadamard Matrices (ADTHM) 2014, in honour of the 70th birthday of Hadi Kharaghani. Thanks to Robert Craigen, and William Martin for valuable discussions, and again to Robert Craigen for presenting Questions 1 and 2 at the workshop on “Algebraic design theory with Hadamard matrices” in Banff in July 2014. Thanks also to the Mathematical Sciences Institute at The Australian National University for the author’s Visiting Fellowship during 2014. Finally, thanks to the anonymous reviewer whose comments have helped to improve this paper.
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Dedicated to Hadi Kharaghani on the occasion on his 70th birthday
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Leopardi, P.C. (2015). Twin Bent Functions and Clifford Algebras. 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_15
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DOI: https://doi.org/10.1007/978-3-319-17729-8_15
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