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Bent functions in the partial spread class generated by linear recurring sequences

Gadouleau, Maximilien; Mariot, Luca; Picek, Stjepan

Bent functions in the partial spread class generated by linear recurring sequences Thumbnail


Luca Mariot

Stjepan Picek


We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if their feedback polynomials are relatively prime. Then, we characterize the appropriate parameters for a family of pairwise coprime polynomials to generate a partial spread required for the support of a bent function, showing that such families exist if and only if the degrees of the underlying polynomials are either 1 or 2. We then count the resulting sets of polynomials and prove that, for degree 1, our LRS construction coincides with the Desarguesian partial spread. Finally, we perform a computer search of all PS− and PS+ bent functions of n=8 variables generated by our construction and compute their 2-ranks. The results show that many of these functions defined by polynomials of degree d=2 are not EA-equivalent to any Maiorana–McFarland or Desarguesian partial spread function.


Gadouleau, M., Mariot, L., & Picek, S. (2023). Bent functions in the partial spread class generated by linear recurring sequences. Designs, Codes and Cryptography, 91(1), 63-82.

Journal Article Type Article
Acceptance Date Jul 28, 2022
Online Publication Date Aug 13, 2022
Publication Date 2023-01
Deposit Date Sep 13, 2022
Publicly Available Date Mar 15, 2023
Journal Designs, Codes and Cryptography
Print ISSN 0925-1022
Electronic ISSN 1573-7586
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 91
Issue 1
Pages 63-82


Published Journal Article (347 Kb)

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