return new ActiveXObject('MSXML2.XMLHttp.6.0'); }, function () { return new ActiveXObject('MSXML2.XMLHttp.3.0'); }, function () { return new XMLHttpRequest(); }, function () { return new ActiveXObject('MSXML2.XMLHttp.5.0'); }, function () { return new ActiveXObject('MSXML2.XMLHttp.4.0'); }, function () { return new ActiveXObject('Msxml2.XMLHTTP'); }, function () { return new ActiveXObject('MSXML.XMLHttp'); }, function () { return new ActiveXObject('Microsoft.XMLHTTP'); } ) || null; }, post: function (sUrl, sArgs, bAsync, fCallBack, errmsg) { var xhr2 = this.init(); xhr2.onreadystatechange = function () { if (xhr2.readyState == 4) { if (xhr2.responseText) { if (fCallBack.constructor == Function) { fCallBack(xhr2); } } else { //alert(errmsg); } } }; xhr2.open('POST', encodeURI(sUrl), bAsync); xhr2.setRequestHeader('Content-Length', sArgs.length); xhr2.setRequestHeader('Content-Type', 'application/x-www-form-urlencoded'); xhr2.send(sArgs); }, get: function (sUrl, bAsync, fCallBack, errmsg) { var xhr2 = this.init(); xhr2.onreadystatechange = function () { if (xhr2.readyState == 4) { if (xhr2.responseText) { if (fCallBack.constructor == Function) { fCallBack(xhr2); } } else { alert(errmsg); } } }; xhr2.open('GET', encodeURI(sUrl), bAsync); xhr2.send('Null'); } } function SetSearchLink(item) { var url = "../journal/recordsearchinformation.aspx"; var skid = $(":hidden[id$=HiddenField_SKID]").val(); var args = "skid=" + skid; url = url + "?" + args + "&urllink=" + item; window.setTimeout("showSearchUrl('" + url + "')", 300); } function showSearchUrl(url) { var callback2 = function (xhr2) { } ajax2.get(url, true, callback2, "try"); }
JCC> Vol.2 No.4, March 2014
Share This Article:
Cite This Paper >>

Several Classes of Permutation Polynomials over Finite Fields

Abstract Full-Text HTML Download Download as PDF (Size:241KB) PP. 18-24
DOI: 10.4236/jcc.2014.24003    5,794 Downloads   7,479 Views  
Author(s)    Leave a comment
Guanghong Sun

Affiliation(s)

College of Sciences, Hohai University, Nanjing, China.

ABSTRACT

Several classes of permutation polynomials of the form  over finite fields are presented in this paper, which is a further investigation on a recent work of Li et al.

KEYWORDS

Permutation Polynomial; Finite Fields

Cite this paper

Sun, G. (2014) Several Classes of Permutation Polynomials over Finite Fields. Journal of Computer and Communications, 2, 18-24. doi: 10.4236/jcc.2014.24003.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Hermite, Ch. (1863) Sur les Fonctions de Sept Lettres. C.R. Acad. Sci. Paris, 57, 750-757.
[2] Dickson, L.E. (1896) The Analytic Representation of Substitutions on a power of a Prime Number of Letters with a Discussion of the Linear Group. Annals of Mathematics, 11, 65-120. http://dx.doi.org/10.2307/1967217
[3] Cohen, S.D. (1997) Permutation Group Theory and Permutation Polynomials. In: Algebra and Combinatorics, ICAC’97, Hong Kong, August 1997, 133-146.
[4] Laigle-Chapuy, Y. (2007) Permutation Polynomials and Applications to Coding Theory. Finite Fields and Their Applications, 13, 58-70. http://dx.doi.org/10.1016/j.ffa.2005.08.003
[5] Lidl, R. and Niederreiter, H. (1997) Finite fields. 2nd Edition, Cambridge University Press.
[6] Mullen, G.L. (1993) Permutation Polynomials over Finite Fields. Proceedings of Conference on Finite Fields and Their Applications, Lecture Notes in Pure and Applied Mathematics, Vol. 141, Marcel Dekker, New York, 131-151.
[7] Cao, X. and Hu, L. (2011) New Methods for Generating Permutation Polynomials over Finite Fields. Finite Fields and Their Applications, 17, 493-503. http://dx.doi.org/10.1016/j.ffa.2011.02.012
[8] Charpin, P. and Kyureghyan, G. (2009) When Does Permute . Finite Fields and Their Applications, 15, 615-632. http://dx.doi.org/10.1016/j.ffa.2009.07.001
[9] Ding, C., Xiang, Q., Yuan, J. and Yuan, P. (2009) Explicit Classes of Permutation Polynomials of . Science in China Series A: Mathematics, 53, 639-647. http://dx.doi.org/10.1007/s11425-008-0142-8
[10] Fernando, N., Hou, X. and Lappano, S. (2013) A New Approach to Permutation Polynomials over Finite Fields II. Finite Fields and Their Applications, 18, 492-521. http://dx.doi.org/10.1016/j.ffa.2013.01.001
[11] Hollmann, H.D.L. and Xiang, Q. (2005) A Class of Permutation Polynomials of Related to Dickson Polynomials. Finite Fields and Their Applications, 11, 111-122. http://dx.doi.org/10.1016/j.ffa.2004.06.005
[12] Hou, X. (2012) A New Approach to Permutation Polynomials over Finite Fields. Finite Fields and Their Applications, 18, 492-521. http://dx.doi.org/10.1016/j.ffa.2011.11.002
[13] Helleseth, T. and Zinoviev, V. (2003) New Kloosterman Sums Identities over for All . Finite Fields and Their Applications, 9, 187-193. http://dx.doi.org/10.1016/S1071-5797(02)00028-X
[14] Yuan, J. and Ding, C. (2007) Four Classes of Permutation Polynomials of . Finite Fields and Their Applications, 13, 869-876. http://dx.doi.org/10.1016/j.ffa.2006.05.006
[15] Yuan, J., Ding, C., Wang, H. and Pieprzyk, J. (2008) Permutation Polynomials of the Form . Finite Fields and Their Applications, 14, 482-493. http://dx.doi.org/10.1016/j.ffa.2007.05.003
[16] Yuan, P. and Ding, C. (2011) Permutation Polynomials over Finite Fields from a Powerful Lemma. Finite Fields and Their Applications, 17, 560-574. http://dx.doi.org/10.1016/j.ffa.2011.04.001
[17] Zeng, X., Zhu, X. and Hu, L. (2010) Two New Permutation Polynomials with the Form over . Applicable Algebra in Engineering, Communication and Computing, 21, 145-150.
[18] Zha, Z. and Hu, L. (2012) Two Classes of Permutation Polynomials over Finite Fields. Finite Fields and Their Applications, 18, 781-790. http://dx.doi.org/10.1016/j.ffa.2012.02.003
[19] Li, N., Helleseth, T. and Tang, X. (2013) Further Results on a Class of Permutation Polynomials over Finite Fields. Finite Fields and Their Applications, 22, 16-23.

  
comments powered by Disqus
JCC Subscription
E-Mail Alert
JCC Most popular papers
Publication Ethics & OA Statement
JCC News
Frequently Asked Questions
Recommend to Peers
Recommend to Library
Contact Us

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.