Properties and applications of preimage distributions of perfect nonlinear functions

Authors:
Chao Li;Qiang Li;San Ling
Affiliations:
Department of Mathematics and System Sciences, Science College, National University of Defence Technology, Changsha, China;Department of Mathematics and System Sciences, Science College, National University of Defence Technology, Changsha, China;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Republic of Singapore
Venue:
IEEE Transactions on Information Theory
Year:
2009

Citing 5
Cited 1

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Abstract

The preimage distributions of perfect nonlinear functions from an Abelian group of order n to an Abelian group of order 3 or 4, respectively, are studied. Based on the properties of the preimage distributions of perfect nonlinear functions from an Abelian group of order 3r to an Abelian group of order 3, the weight distributions of the ternary linear codes CΠ from the perfect nonlinear functions Π(x) from F3r to itself are determined. These results suggest that two open problems, proposed by Carlet, Ding, and Yuan in 2005 and 2006, respectively, are answered.