Abstract
In this paper we provide new families of balanced symmetric functions over any finite field. We also generalize a conjecture of Cusick, Li, and Stǎnicǎ about the non-balancedness of elementary symmetric Boolean functions to any finite field and prove part of our conjecture.
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Acknowledgements
The authors appreciate the comments and suggestions to the paper made by one of the referees and the additional suggestions and a correction made by Alexander Pott. All of them helped to improve the paper. The third author was partially supported as a student by NSF-DUE 1356474 and the Mellon-Mays Undergraduate Fellowship. The fourth author acknowledges the partial support of UPR-FIPI 1890015.00.
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Communicated by A. Pott.
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Arce-Nazario, R.A., Castro, F.N., González, O.E. et al. New families of balanced symmetric functions and a generalization of Cusick, Li and Stǎnicǎ’s conjecture. Des. Codes Cryptogr. 86, 693–701 (2018). https://doi.org/10.1007/s10623-017-0351-7
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DOI: https://doi.org/10.1007/s10623-017-0351-7