Good Second-Order Nonlinearity of a Subclass of Kasami Function on Five, Seven and Nine Variables

Abstract

In this paper we find the lower bounds of second-order nonlinearity of a subclass of kasami function on five, seven and nine variables. It is also shown that these bounds are better than the bounds obtained by Li, Hu and Gao (http: // eprint.iacr.org/2010/009.pdf.). We also compared these bounds with the maximum known hamming distance of second-order Reed-Muler codes.