Properties and Applications of Preimage Distributions of Perfect Nonlinear Functions
Chao Li, Qiang Li, San Ling · IEEE Transactions on Information Theory · 2009
The preimage distributions of perfect nonlinear functions from an Abelian group of ordernto an Abelian group of order3or4, respectively, are studied. Based on the properties of the preimage distributions of perfect nonlinear functions from an Abelian group of order3rto an Abelian group of order3, the weight distributions of the ternary linear codesCPifrom the perfect nonlinear functionsPi(x) fromF3rto itself are determined. These results suggest that two open problems, proposed by Carlet, Ding, and Yuan in 2005 and 2006, respectively, are answered.