Geometric and design-theoretic aspects of semibent functions I

The two parts of this paper consider combinatorial and geometric aspects of semibent functions. In the first part of this note we obtain 2-designs from semibent functions and we characterize their automorphism groups. In the second part semibent functions of partial spread type with a linear structure are investigated.

[1]  Bruno Codenotti,et al.  Spectral Analysis of Boolean Functions as a Graph Eigenvalue Problem , 1999, IEEE Trans. Computers.

[2]  M. Aschbacher.  Finite Group Theory: Representations of groups on groups , 2000 .

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

[4]  Xiang-dong Hou.  Cubic bent functions , 1998, Discret. Math..

[5]  J. Dieudonné,et al.  La géométrie des groupes classiques , 1963 .

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

[7]  R. Dye.  Partitions and their stabilizers for line complexes and quadrics , 1977 .

[8]  Anne Canteaut,et al.  On cryptographic properties of the cosets of R(1, m) , 2001, IEEE Trans. Inf. Theory.

[9]  A. Canteaut,et al.  Decomposing bent functions , 2002, Proceedings IEEE International Symposium on Information Theory,.

[10]  Yuliang Zheng,et al.  On plateaued functions , 1999, IEEE Trans. Inf. Theory.

[11]  Hans-Dieter Lüke,et al.  Perfect ternary arrays , 1990, IEEE Trans. Inf. Theory.

[12]  A. Pott,et al.  Difference sets, sequences and their correlation properties , 1999 .

[13]  Zhong-Qi Ma,et al.  THE SYMPLECTIC GROUPS , 2004 .

[14]  Yuliang Zheng,et al.  Relationships between Bent Functions and Complementary Plateaued Functions , 1999, ICISC.

[15]  William M. Kantor,et al.  Symplectic groups, symmetric designs, and line ovals , 1975 .

[16]  William M. Kantor,et al.  Spreads, Translation Planes and Kerdock Sets. I , 1982 .

[17]  L. Grove,et al.  Classical Groups and Geometric Algebra , 2001 .

[18]  H. B. Mann.  Difference sets in elementary abelian groups , 1965 .

[19]  José Ranilla,et al.  Classification of semifields of order 64 , 2009 .

[20]  Kwangjo Kim,et al.  Semi-bent Functions , 1994, ASIACRYPT.

[21]  Claude Carlet,et al.  A Larger Class of Cryptographic Boolean Functions via a Study of the Maiorana-McFarland Construction , 2002, CRYPTO.

[22]  José Ranilla,et al.  Determination of division algebras with 243 elements , 2010, Finite Fields Their Appl..

[23]  B. Huppert.  Endliche Gruppen I , 1967 .

[24]  Claude Carlet.  Partially-bent functions , 1993, Des. Codes Cryptogr..

[25]  William M. Kantor,et al.  Exponential numbers of two-weight codes, difference sets and symmetric designs , 1983, Discret. Math..

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

[27]  P. Dembowski,et al.  Some characterizations of finite projective spaces , 1960 .

[28]  Ulrich Dempwolff,et al.  Automorphisms and Equivalence of Bent Functions and of Difference Sets in Elementary Abelian 2-Groups , 2006 .