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

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.