Maximum nonlinearity of symmetric Boolean functions on odd number of variables |
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| Authors: | Maitra S. Sarkar P. |
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| Affiliation: | Comput. & Stat. Service Center, Indian Stat. Inst., Calcutta; |
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| Abstract: | In this correspondence, we establish that for odd n, the maximum nonlinearity achievable by an n-variable symmetric Boolean function is 2/sup n-1/-2/sup (n-1)///sup 2/ and characterize the set of functions which achieve this value of nonlinearity. In particular, we show that for each odd n/spl ges/3, there are exactly four possible symmetric Boolean functions achieving the nonlinearity 2/sup n-1/-2/sup (n-1)/2/. |
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