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Advances in Mathematics of Communications (AMC)
 

Asymptotic lower bound on the algebraic immunity of random balanced multi-output Boolean functions

Pages: 197 - 217, Volume 7, Issue 2, May 2013      doi:10.3934/amc.2013.7.197

 
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Claude Carlet - LAGA, Universities of Paris 8 and Paris 13, CNRS, France (email)
Brahim Merabet - Department of Algebraic and number theory, University of Sciences and Technology, Houari Boumedienne, Algiers, Algeria, and University of Kasdi Merbah, Ouargla, Algeria (email)

Abstract: This paper extends the work of F. Didier (IEEE Transactions on Information Theory, Vol. 52(10): 4496-4503, October 2006) on the algebraic immunity of random balanced Boolean functions, into an asymptotic lower bound on the algebraic immunity of random balanced multi-output Boolean functions.

Keywords:  Boolean functions, vectorial functions, erasure channel, generalized Hamming distances, Reed-Muller codes, algebraic immunity.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: January 2013;      Available Online: May 2013.

 References