Properties and applications of preimage distributions of perfect nonlinear functions
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 ord...
| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
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2013
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| Online Access: | https://hdl.handle.net/10356/96299 http://hdl.handle.net/10220/9855 |
| _version_ | 1826129400713707520 |
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| author | Li, Chao Li, Qiang Ling, San |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Li, Chao Li, Qiang Ling, San |
| author_sort | Li, Chao |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T07:39:58Z |
| format | Journal Article |
| id | ntu-10356/96299 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:39:58Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/962992023-02-28T19:39:28Z Properties and applications of preimage distributions of perfect nonlinear functions Li, Chao Li, Qiang Ling, San School of Physical and Mathematical Sciences DRNTU::Science::Mathematics 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. Accepted version 2013-04-23T07:39:19Z 2019-12-06T19:28:26Z 2013-04-23T07:39:19Z 2019-12-06T19:28:26Z 2009 2009 Journal Article 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. 0018-9448 https://hdl.handle.net/10356/96299 http://hdl.handle.net/10220/9855 10.1109/TIT.2008.2008126 en IEEE transactions on information theory © 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]. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics Li, Chao Li, Qiang Ling, San Properties and applications of preimage distributions of perfect nonlinear functions |
| title | Properties and applications of preimage distributions of perfect nonlinear functions |
| title_full | Properties and applications of preimage distributions of perfect nonlinear functions |
| title_fullStr | Properties and applications of preimage distributions of perfect nonlinear functions |
| title_full_unstemmed | Properties and applications of preimage distributions of perfect nonlinear functions |
| title_short | Properties and applications of preimage distributions of perfect nonlinear functions |
| title_sort | properties and applications of preimage distributions of perfect nonlinear functions |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/96299 http://hdl.handle.net/10220/9855 |
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