Crooked Functions, Bent Functions, and Distance Regular Graphs

@article{Bending1998CrookedFB,
title={Crooked Functions, Bent Functions, and Distance Regular Graphs},
author={T. D. Bending and Dmitry Fon-Der-Flaass},
journal={Electr. J. Comb.},
year={1998},
volume={5}
}

Let V and W be n-dimensional vector spaces over GF (2). A mapping Q : V →W is called crooked if it satisfies the following three properties: Q(0) = 0; Q(x) +Q(y) +Q(z) +Q(x+ y + z) 6= 0 for any three distinct x, y, z; Q(x) +Q(y) +Q(z) +Q(x+ a) +Q(y + a) +Q(z + a) 6= 0 if a 6= 0 (x, y, z arbitrary). We show that every crooked function gives rise to a distance regular graph of diameter 3 having λ = 0 and μ = 2 which is a cover of the complete graph. Our approach is a generalization of a recent… CONTINUE READING