Papers › Bent Functions in the Partial Spread Class Generated by Linear Recurring Sequences
Bent Functions in the Partial Spread Class Generated by Linear Recurring Sequences
Maximilien Gadouleau, Luca Mariot, Stjepan Picek
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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 is 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 b=2 are not EA-equivalent to any Maiorana-McFarland or Desarguesian partial spread function.
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