Maximum nonlinearity of symmetric Boolean functions on odd number of variables

2002/09/01 by S. Maitra, Subhamoy Maitra, P. Sarkar +1 · 3 citations
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cellular Automata and Applications

paper · doi:10.1109/tit.2002.801482

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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• Balanced Symmetric Functions over GF(p)
• Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number of Variables
• A Note on a Conjecture for Balanced Elementary Symmetric Boolean Functions

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