Title :
Z4-version of the binary Maiorana-McFarland bent functions
Author_Institution :
GECT, Toulon Univ., La Garde, France
Abstract :
We introduce a one-to-one connection between a family M4 of functions defined over the Galois ring R=GR(4,m) of cardinality 4m and the binary Maiorana-McFarland family of bent functions. This gives rise to difference sets in the additive group of R=GR(4,m). On the other hand, we show that, if D is one of these new quaternary difference sets and if Φ is the Gray map of R into F22m, then Φ(D) is a difference set of (F22m,+)
Keywords :
Boolean functions; Galois fields; group theory; information theory; Galois ring; Gray map; Z4-version; additive group; binary Maiorana-McFarland bent functions; difference sets; one-to-one connection; quaternary difference sets; Fourier transforms; Galois fields;
Conference_Titel :
Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
0-7803-5000-6
DOI :
10.1109/ISIT.1998.709006
