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International Journal of Mathematics and Mathematical Sciences
Volume 2016 (2016), Article ID 6093219, 7 pages
http://dx.doi.org/10.1155/2016/6093219
Research Article

Characterization and Enumeration of Good Punctured Polynomials over Finite Fields

1Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand
2Department of Mathematics, Mahidol Wittayanusorn School, Nakhon Pathom 73170, Thailand

Received 25 November 2015; Revised 3 March 2016; Accepted 6 March 2016

Academic Editor: Shyam L. Kalla

Copyright © 2016 Somphong Jitman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A family of good punctured polynomials is introduced. The complete characterization and enumeration of such polynomials are given over the binary field . Over a nonbinary finite field , the set of good punctured polynomials of degree less than or equal to are completely determined. For , constructive lower bounds of the number of good punctured polynomials of degree over are given.