On the Covering Radius of Second Order Binary Reed-Muller Code in the Set of Resilient Boolean Functions
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چکیده
Let Rt,n denote the set of t-resilient Boolean functions of n variables. First, we prove that the covering radius of the binary ReedMuller 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.
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تاریخ انتشار 2003