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A new construction of bent functions based on \({\mathbb{Z}}\) -bent functions

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Abstract

Dobbertin has embedded the problem of construction of bent functions in a recursive framework by using a generalization of bent functions called \({\mathbb{Z}}\) -bent functions. Following his ideas, we generalize the construction of partial spreads bent functions to partial spreads \({\mathbb{Z}}\) -bent functions of arbitrary level. Furthermore, we show how these partial spreads \({\mathbb{Z}}\) -bent functions give rise to a new construction of (classical) bent functions. Further, we construct a bent function on 8 variables which is inequivalent to all Maiorana–McFarland as well as PS ap type bents. It is also shown that all bent functions on 6 variables, up to equivalence, can be obtained by our construction.

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Correspondence to Sugata Gangopadhyay.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

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Gangopadhyay, S., Joshi, A., Leander, G. et al. A new construction of bent functions based on \({\mathbb{Z}}\) -bent functions. Des. Codes Cryptogr. 66, 243–256 (2013). https://doi.org/10.1007/s10623-012-9687-1

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  • DOI: https://doi.org/10.1007/s10623-012-9687-1

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