Abstract
The minimum distance between bent and resilient functions is studied. This problem is converted into two problems. One is to construct a special matrix, which leads to a combinatorial problem; the other is the existence of bent functions with specified types. Then the relation of these two problems is studied. For the 1-resilient functions, we get a solution to the first combinatorial problem. By using this solution and the relation of the two problems, we present a formula on the lower bound of the minimum distance of bent and 1-resilient functions. For the latter problem, we point out the limitation of the usage of the Maiorana-McFarland type bent functions, and the necessity to study the existence of bent functions with special property which we call partial symmetric. At last, we give some results on the nonexistence of some partial symmetric bent functions.
This work is supported by the Natural Science Foundation of China(NO.60573028, 60803156) and the open research fund of National Mobile Communications Research Laboratory of Southeast University(W200807).
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Qu, L., Li, C. (2009). Minimum Distance between Bent and Resilient Boolean Functions. In: Chee, Y.M., Li, C., Ling, S., Wang, H., Xing, C. (eds) Coding and Cryptology. IWCC 2009. Lecture Notes in Computer Science, vol 5557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01877-0_18
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DOI: https://doi.org/10.1007/978-3-642-01877-0_18
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