Constructing symmetric boolean functions with maximum algebraic immunity

Authors:
Longjiang Qu;Keqin Feng;Feng Liu;Lei Wang
Affiliations:
Department of Mathematics and System Science, Science College, National University of Defence Technology, ChangSha, China and National Mobile Communications Research Laboratory, Southeast Universi ...;Department of Mathematics, Tsinghua University, Beijing, China;Department of Mathematics, Tsinghua University, Beijing, China;Department of Mathematics, Georgia Institute of Technology, Atlanta, GA
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

Symmetric Boolean functions with even variables 2k and maximum algebraic immunity AI(f) = k have been constructed in Braeken's thesis (2006). In this paper, we show more constructions of such Boolean functions including the generalization of a result and prove a conjecture raised in Braeken's thesis (2006).