Abstract
Let \(\mathcal R_{t,n}\) 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 \(\mathcal R_{t,6}\), 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 \(\mathcal R_{3,7}\) is 32. We derive a new lower bound for the covering radius of the Reed-Muller code RM(2,n) in the set \(\mathcal R_{n-1,4}\). Finally, we present new lower bounds in the sets \(\mathcal R_{t,7}\), t=0,1,2.
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Borissov, Y., Braeken, A., Nikova, S., Preneel, B. (2003). On the Covering Radius of Second Order Binary Reed-Muller Code in the Set of Resilient Boolean Functions. In: Paterson, K.G. (eds) Cryptography and Coding. Cryptography and Coding 2003. Lecture Notes in Computer Science, vol 2898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40974-8_8
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DOI: https://doi.org/10.1007/978-3-540-40974-8_8
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