论文信息 - Counting Partial Spread Functions in Eight Variables

Counting Partial Spread Functions in Eight Variables

In this paper we report the following computational results on partial spread functions in eight variables: (i) the numbers of equivalence classes of partial spread functions (in eight variables) of all possible orders; (ii) the total number of partial spread bent functions in eight variables; (iii) the distribution of the cardinalities of stabilizers (in GL(8, F2)) of partial spread bent functions in eight variables. The computational method is also described.

Philippe Langevin | Xiang-dong Hou | P. Langevin | Xiang-dong Hou

[1] J. Dillon. Elementary Hadamard Difference Sets , 1974 .

[2] Arthur Reifart. The classification of the translation planes of order 16, II , 1983 .

[3] U. Dempwolff,et al. The classification of the translation planes of order 16, I , 1983 .

[4] Xiang-dong Hou. GL(m, 2) acting on R(r, m)/R(r-1, m) , 1996, Discret. Math..

[5] Philippe Langevin,et al. Results on Bent Functions , 1997, J. Comb. Theory, Ser. A.

[6] William Millan,et al. Linear Redundancy in S-Boxes , 2003, FSE.

[7] C. Carlet. On the Secondary Constructions of Resilient and Bent Functions , 2004 .

[8] Nils Gregor Leander. Normality of Bent Functions Monomial-and Binomial-Bent Functions , 2004 .

[9] Claude Carlet,et al. On Bent and Highly Nonlinear Balanced/Resilient Functions and Their Algebraic Immunities , 2006, AAECC.

[10] Anne Canteaut,et al. Construction of bent functions via Niho power functions , 2006, J. Comb. Theory, Ser. A.

[11] Timo Neumann,et al. BENT FUNCTIONS , 2006 .

[12] G. Leander,et al. Classification of Boolean Quartic Forms in eight variables , 2008 .

[13] Claude Carlet,et al. Boolean Functions for Cryptography and Error-Correcting Codes , 2010, Boolean Models and Methods.