@article { ,
title = {Bent functions in the partial spread class generated by linear recurring sequences},
abstract = {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.},
doi = {10.1007/s10623-022-01097-1},
eissn = {1573-7586},
issn = {0925-1022},
issue = {1},
journal = {Designs, Codes and Cryptography},
note = {EPrint Processing Status: Full text deposited in DRO},
pages = {63-82},
publicationstatus = {Published},
publisher = {Springer},
url = {https://durham-repository.worktribe.com/output/1194634},
volume = {91},
year = {2023},
author = {Gadouleau, Maximilien and Mariot, Luca and Picek, Stjepan}
}