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|Title:||Properties and applications of preimage distributions of perfect nonlinear functions||Authors:||Li, Chao
|Keywords:||DRNTU::Science::Mathematics||Issue Date:||2009||Source:||Li, C., Li, Q., & Ling, S. (2009). Properties and Applications of Preimage Distributions of Perfect Nonlinear Functions. IEEE Transactions on Information Theory, 55(1), 64-69.||Series/Report no.:||IEEE transactions on information theory||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 C Pi from the perfect nonlinear functions Pi(x) from F 3 r to itself are determined. These results suggest that two open problems, proposed by Carlet, Ding, and Yuan in 2005 and 2006, respectively, are answered.||URI:||https://hdl.handle.net/10356/96299
|ISSN:||0018-9448||DOI:||10.1109/TIT.2008.2008126||Rights:||© 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [http://dx.doi.org/10.1109/TIT.2008.2008126].||Fulltext Permission:||open||Fulltext Availability:||With Fulltext|
|Appears in Collections:||SPMS Journal Articles|
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