On the covering radius of second order binary Reed-Muller code in the set of resilient Boolean functions

Abstract

Let Rt,n denote the set of t-resilient Boolean functions of n variables. First, we prove that the covering radius of the binary Reed-Muller code RM(2,6) in the sets Rt,6 t = 0,1,2 is 16. Second, we show that the covering radius of the binary Reed-Muller code RM(2, 7) in the set R3,7 is 32. We derive a new lower bound for the covering radius of the Reed-Muller code RM(2,n) in the set Rn-4,n. Finally, we present new lower bounds in the sets Rt,7, t = 0, 1, 2. © Springer-Verlag Berlin Heidelberg 2003.