Abstract
We construct an infinite family of \(1\frac{1}{2}\)-difference sets in non-cyclic abelian \(p\)-groups. In particular, we examine the construction in \(2\)-groups to discover the useful relationship between \(1\frac{1}{2}\)-difference sets and certain Boolean functions.
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Notes
It is often known as a tactical configuration.
Bose [2] studied \(1\frac{1}{2}\)-designs and called them partial geometric designs.
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Acknowledgments
I would like to thank the anonymous referees for their insightful comments on improving the quality of the paper. This work was supported in part by NSF Grant CCF-1018148.
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Communicated by A. Pott.
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Olmez, O. Plateaued functions and one-and-half difference sets. Des. Codes Cryptogr. 76, 537–549 (2015). https://doi.org/10.1007/s10623-014-9975-z
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DOI: https://doi.org/10.1007/s10623-014-9975-z
Keywords
- \(1\frac{1}{2}\)-Design
- \(1\frac{1}{2}\)-Difference set
- Plateaued function
- Bent function
- Semibent function