A note on linearized polynomials and the dimension of their kernels
Recently explicit representations of the class of linearized permutation polynomials and the number of such polynomials were given in Zhou (2008) [4] and Yuan and Zeng (2011) [3]. In this paper, we generalize this result to linearized polynomials with kernel of any given dimension, solving an open p...
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2013
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| Online Access: | https://hdl.handle.net/10356/96078 http://hdl.handle.net/10220/11195 |
| _version_ | 1826111939819864064 |
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| author | Ling, San Qu, Longjiang |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Ling, San Qu, Longjiang |
| author_sort | Ling, San |
| collection | NTU |
| description | Recently explicit representations of the class of linearized permutation polynomials and the number of such polynomials were given in Zhou (2008) [4] and Yuan and Zeng (2011) [3]. In this paper, we generalize this result to linearized polynomials with kernel of any given dimension, solving an open problem in Charpin and Kyureghyan (2009) [1]. Moreover, more explicit representations of such polynomials are given and several classes of explicit linearized polynomials with kernel of any given dimension are presented. |
| first_indexed | 2024-10-01T02:58:44Z |
| format | Journal Article |
| id | ntu-10356/96078 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:58:44Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/960782020-03-07T12:31:29Z A note on linearized polynomials and the dimension of their kernels Ling, San Qu, Longjiang School of Physical and Mathematical Sciences DRNTU::Science::Mathematics Recently explicit representations of the class of linearized permutation polynomials and the number of such polynomials were given in Zhou (2008) [4] and Yuan and Zeng (2011) [3]. In this paper, we generalize this result to linearized polynomials with kernel of any given dimension, solving an open problem in Charpin and Kyureghyan (2009) [1]. Moreover, more explicit representations of such polynomials are given and several classes of explicit linearized polynomials with kernel of any given dimension are presented. 2013-07-11T04:33:04Z 2019-12-06T19:25:18Z 2013-07-11T04:33:04Z 2019-12-06T19:25:18Z 2011 2011 Journal Article https://hdl.handle.net/10356/96078 http://hdl.handle.net/10220/11195 10.1016/j.ffa.2011.06.002 en Finite fields and their applications © 2011 Elsevier Inc. |
| spellingShingle | DRNTU::Science::Mathematics Ling, San Qu, Longjiang A note on linearized polynomials and the dimension of their kernels |
| title | A note on linearized polynomials and the dimension of their kernels |
| title_full | A note on linearized polynomials and the dimension of their kernels |
| title_fullStr | A note on linearized polynomials and the dimension of their kernels |
| title_full_unstemmed | A note on linearized polynomials and the dimension of their kernels |
| title_short | A note on linearized polynomials and the dimension of their kernels |
| title_sort | note on linearized polynomials and the dimension of their kernels |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/96078 http://hdl.handle.net/10220/11195 |
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