New results on permutation polynomials over finite fields
In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms $L(x)+\sum_{j=1}^k \gamma_jh_j(f_j(x))$ and $x+\sum_{j=1}^k\gamma_jf_j(x)$. These generalize the results obtained by Kyure...
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| creator | Qin, Xiaoer Qian, Guoyou Hong, Shaofang |
| description | In this paper, we get several new results on permutation polynomials over
finite fields. First, by using the linear translator, we construct permutation
polynomials of the forms $L(x)+\sum_{j=1}^k \gamma_jh_j(f_j(x))$ and
$x+\sum_{j=1}^k\gamma_jf_j(x)$. These generalize the results obtained by
Kyureghyan in 2011. Consequently, we characterize permutation polynomials of
the form $L(x)+\sum_{i=1} ^l\gamma_i {\rm Tr}_{{\bf F}_{q^m}/{\bf
F}_{q}}(h_i(x))$, which extends a theorem of Charpin and Kyureghyan obtained in
2009. |
| doi_str_mv | 10.48550/arxiv.1403.6012 |
| format | Article |
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finite fields. First, by using the linear translator, we construct permutation
polynomials of the forms $L(x)+\sum_{j=1}^k \gamma_jh_j(f_j(x))$ and
$x+\sum_{j=1}^k\gamma_jf_j(x)$. These generalize the results obtained by
Kyureghyan in 2011. Consequently, we characterize permutation polynomials of
the form $L(x)+\sum_{i=1} ^l\gamma_i {\rm Tr}_{{\bf F}_{q^m}/{\bf
F}_{q}}(h_i(x))$, which extends a theorem of Charpin and Kyureghyan obtained in
2009.</description><identifier>DOI: 10.48550/arxiv.1403.6012</identifier><language>eng</language><subject>Mathematics - Number Theory</subject><creationdate>2014-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1403.6012$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1403.6012$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Qin, Xiaoer</creatorcontrib><creatorcontrib>Qian, Guoyou</creatorcontrib><creatorcontrib>Hong, Shaofang</creatorcontrib><title>New results on permutation polynomials over finite fields</title><description>In this paper, we get several new results on permutation polynomials over
finite fields. First, by using the linear translator, we construct permutation
polynomials of the forms $L(x)+\sum_{j=1}^k \gamma_jh_j(f_j(x))$ and
$x+\sum_{j=1}^k\gamma_jf_j(x)$. These generalize the results obtained by
Kyureghyan in 2011. Consequently, we characterize permutation polynomials of
the form $L(x)+\sum_{i=1} ^l\gamma_i {\rm Tr}_{{\bf F}_{q^m}/{\bf
F}_{q}}(h_i(x))$, which extends a theorem of Charpin and Kyureghyan obtained in
2009.</description><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8sKwjAURLNxIerelfQHWtPENL1LEV8gunFfbvQGAn1IWl9_b6quzsDAMIexacqTRa4Un6N_uUeSLrhMMp6KIYMjPSNP7b3s2qipoxv56t5h5_rclO-6qRyWoXqQj6yrXUcBVF7bMRvY0NDkzxE7b9bn1S4-nLb71fIQY6ZEnCMnZSRJroVFQKvJXhA1iFxo0hcE0EZKkSkDBGgg0IqryTAACeSIzX6z3-vFzbsK_bvoFYpeQX4AH8dCZg</recordid><startdate>20140324</startdate><enddate>20140324</enddate><creator>Qin, Xiaoer</creator><creator>Qian, Guoyou</creator><creator>Hong, Shaofang</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20140324</creationdate><title>New results on permutation polynomials over finite fields</title><author>Qin, Xiaoer ; Qian, Guoyou ; Hong, Shaofang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a652-8a0e5b3e3072fa9af7efcaa792827e7ca997b33265b9e9ab95b9f2db6a9f2ae93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Qin, Xiaoer</creatorcontrib><creatorcontrib>Qian, Guoyou</creatorcontrib><creatorcontrib>Hong, Shaofang</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Qin, Xiaoer</au><au>Qian, Guoyou</au><au>Hong, Shaofang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New results on permutation polynomials over finite fields</atitle><date>2014-03-24</date><risdate>2014</risdate><abstract>In this paper, we get several new results on permutation polynomials over
finite fields. First, by using the linear translator, we construct permutation
polynomials of the forms $L(x)+\sum_{j=1}^k \gamma_jh_j(f_j(x))$ and
$x+\sum_{j=1}^k\gamma_jf_j(x)$. These generalize the results obtained by
Kyureghyan in 2011. Consequently, we characterize permutation polynomials of
the form $L(x)+\sum_{i=1} ^l\gamma_i {\rm Tr}_{{\bf F}_{q^m}/{\bf
F}_{q}}(h_i(x))$, which extends a theorem of Charpin and Kyureghyan obtained in
2009.</abstract><doi>10.48550/arxiv.1403.6012</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Number Theory |
| title | New results on permutation polynomials over finite fields |
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