论文信息 - On the Symmetric Negabent Boolean Functions

On the Symmetric Negabent Boolean Functions

We study the negabent Boolean functions which are symmetric. The Boolean function which has equal absolute spectral values under the nega-Hadamard transform is called a negabent function. For a bent function, the absolute spectral values are the same under the Hadamard-Walsh transform. Unlike bent functions, negabent functions can exist on odd number of variables. Moreover, all the affine functions are negabent. We prove that a symmetric Boolean function is negabent if and only if it is affine.

Sumanta Sarkar

[1] Matthew G. Parker,et al. One and Two-Variable Interlace Polynomials: A Spectral Interpretation , 2005, WCC.

[2] Matthew G. Parker,et al. Negabent Functions in the Maiorana-McFarland Class , 2008, SETA.

[3] Matthew G. Parker,et al. On Boolean Functions Which Are Bent and Negabent , 2007, SSC.

[4] F. MacWilliams,et al. The Theory of Error-Correcting Codes , 1977 .

[5] M. Parker. Constabent properties of Golay-Davis-Jedwab sequences , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[6] O. S. Rothaus,et al. On "Bent" Functions , 1976, J. Comb. Theory, Ser. A.

[7] Robert B. Ash,et al. Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[8] Matthew G. Parker,et al. Generalized Bent Criteria for Boolean Functions (I) , 2005, IEEE Transactions on Information Theory.

[9] Solomon W. Golomb,et al. Sequences, Subsequences, and Consequences, International Workshop, SSC 2007, Los Angeles, CA, USA, May 31 - June 2, 2007, Revised Invited Papers , 2007, SSC.

[10] Petr Savický. On the Bent Boolean Functions That are Symmetric , 1994, Eur. J. Comb..