On the Covering Radius of the Second Order Reed-Muller Code of Length 128
نویسنده
چکیده
In 1981, Schatz proved that the covering radius of the binary ReedMuller code RM(2, 6) is 18. For RM(2, 7), we only know that its covering radius is between 40 and 44. In this paper, we prove that the covering radius of the binary Reed-Muller code RM(2, 7) is at most 42. Moreover, we give a sufficient and necessary condition for Boolean functions of 7-variable to achieve the second-order nonlinearity 42.
منابع مشابه
On the Covering Radius of Second Order Binary Reed-Muller Code in the Set of Resilient Boolean Functions
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....
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عنوان ژورنال:
- CoRR
دوره abs/1510.08535 شماره
صفحات -
تاریخ انتشار 2015