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International Journal of Mathematics and Mathematical Sciences
Volume 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.

Linked References

  1. B. Kalantari, Polynomial Root-Finding and Polynomiography, World Scientific Publishing, River Edge, NJ, USA, 2008. View at MathSciNet
  2. V. Y. Pan and A.-L. Zheng, “New progress in real and complex polynomial root-finding,” Computers & Mathematics with Applications, vol. 61, no. 5, pp. 1305–1334, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. W. K. Nicholson, Introduction to Abstract Algebra, John Wiley & Sons, New York, NY, USA, 2012.
  4. C. C. Pinter, A Book of Abstract Algebra, Dover, Mineola, NY, USA, 2nd edition, 2010. View at MathSciNet
  5. R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, Cambridge, UK, 1997. View at MathSciNet
  6. E. Sangwisut, S. Jitman, S. Ling, and P. Udomkavanich, “Hulls of cyclic and negacyclic codes over finite fields,” Finite Fields and their Applications, vol. 33, pp. 232–257, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. A. Akbary and Q. Wang, “On some permutation polynomials over finite fields,” International Journal of Mathematics and Mathematical Sciences, vol. 2005, no. 16, pp. 2631–2640, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. R. A. Mollin and C. Small, “On permutation polynomials over finite fields,” International Journal of Mathematics and Mathematical Sciences, vol. 10, no. 3, pp. 535–543, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Sahni and P. T. Sehgal, “Hermitian self-orthogonal constacyclic codes over finite fields,” Journal of Discrete Mathematics, vol. 2014, Article ID 985387, 7 pages, 2014. View at Publisher · View at Google Scholar
  10. E. R. Berlekamp, “Factoring polynomials over finite fields,” The Bell System Technical Journal, vol. 46, pp. 1853–1859, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. C. R. Butler, “On the reducibility of polynomials over a finite field,” The Quarterly Journal of Mathematics, vol. 5, pp. 102–107, 1954. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J.-M. Couveignes and R. Lercier, “Fast construction of irreducible polynomials over finite fields,” Israel Journal of Mathematics, vol. 194, no. 1, pp. 77–105, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. A. Knopfmacher and J. Knopfmacher, “Counting polynomials with a given number of zeros in a finite field,” Linear and Multilinear Algebra, vol. 26, no. 4, pp. 287–292, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  14. D. S. Dummit and R. M. Foote, Abstract Algebra, John Wiley & Sons, New York, NY, USA, 3rd edition, 2003.